Реферат: Показательно степенные уравнения и неравенства
--PAGE_BREAK--4. При <shape id="_x0000_i1056" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image064.wmz» o:><img width=«56» height=«23» src=«dopb84565.zip» v:shapes="_x0000_i1056"> и <shape id="_x0000_i1057" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image066.wmz» o:><img width=«64» height=«23» src=«dopb84566.zip» v:shapes="_x0000_i1057"> решаем уравнение f(x)= g(x) и подстановкой полученных результатов в исходное уравнение отсекаем посторонние корни.Примеры решения показательно-степенных уравнений.
Пример №1.
<shape id="_x0000_i1058" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image068.wmz» o:><img width=«119» height=«28» src=«dopb84567.zip» v:shapes="_x0000_i1058">
Решение
1) x – 3 = 0, x = 3. т.к. 3 > 0, и 32 > 0, то x1 = 3 — это решение.
2) x – 3 = 1, x2 = 4.
3) x – 3 = -1, x = 2. Оба показателя четные. Это решение x3 = 1.
4) x – 3 ≠ 0 и x ≠ ± 1. x = x2, x = 0 или x = 1. При x = 0, (-3)0 = (-3)0–верно это решение x4 = 0. При x = 1, (-2)1 = (-2)1 – верно это решение x5 = 1.
Ответ: 0, 1, 2, 3, 4.
Пример №2.
<shape id="_x0000_i1059" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image070.wmz» o:><img width=«240» height=«55» src=«dopb84568.zip» v:shapes="_x0000_i1059">
Решение
По определению арифметического квадратного корня: x – 1 ≥ 0, x ≥ 1.
1) x – 1 = 0 или x = 1, <shape id="_x0000_i1060" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image072.wmz» o:><img width=«45» height=«24» src=«dopb84569.zip» v:shapes="_x0000_i1060"> = 0, 00 это не решение.
2) x – 1 = 1 x 1 = 2.
3) x – 1 = -1 x 2 = 0 не подходит в ОДЗ.
4) <shape id="_x0000_i1061" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image074.wmz» o:><img width=«45» height=«24» src=«dopb84569.zip» v:shapes="_x0000_i1061"> = <shape id="_x0000_i1062" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image075.wmz» o:><img width=«36» height=«41» src=«dopb84570.zip» v:shapes="_x0000_i1062">
<shape id="_x0000_i1063" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image077.wmz» o:><img width=«103» height=«49» src=«dopb84571.zip» v:shapes="_x0000_i1063"> <shape id="_x0000_i1064" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image079.wmz» o:><img width=«121» height=«44» src=«dopb84572.zip» v:shapes="_x0000_i1064">
<shape id="_x0000_i1065" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image081.wmz» o:><img width=«153» height=«44» src=«dopb84573.zip» v:shapes="_x0000_i1065">
<shape id="_x0000_i1066" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image083.wmz» o:><img width=«156» height=«44» src=«dopb84574.zip» v:shapes="_x0000_i1066">
<shape id="_x0000_i1067" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image085.wmz» o:><img width=«100» height=«21» src=«dopb84575.zip» v:shapes="_x0000_i1067">
Д = (-2) – 4*1*5 = 4 – 20 = -16 – корней нет.
Ответ: 2.
Пример №3.
<shape id="_x0000_i1068" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image087.wmz» o:><img width=«182» height=«47» src=«dopb84576.zip» v:shapes="_x0000_i1068">
Решение
1) <shape id="_x0000_i1069" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image089.wmz» o:><img width=«80» height=«24» src=«dopb84577.zip» v:shapes="_x0000_i1069"> = 0 решения нет, т.к. 0 в любой степени не равен 1.
2) <shape id="_x0000_i1070" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image091.wmz» o:><img width=«83» height=«24» src=«dopb84578.zip» v:shapes="_x0000_i1070"> ≠ 0 т.е. <shape id="_x0000_i1071" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image093.wmz» o:><img width=«90» height=«47» src=«dopb84579.zip» v:shapes="_x0000_i1071">. Тогда можем записать:
<shape id="_x0000_i1072" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image095.wmz» o:><img width=«213» height=«34» src=«dopb84580.zip» v:shapes="_x0000_i1072">
3) <shape id="_x0000_i1073" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image089.wmz» o:><img width=«80» height=«24» src=«dopb84577.zip» v:shapes="_x0000_i1073"> = 1. <shape id="_x0000_i1074" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image097.wmz» o:><img width=«87» height=«24» src=«dopb84581.zip» v:shapes="_x0000_i1074"> = 0
<shape id="_x0000_i1075" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image099.wmz» o:><img width=«51» height=«23» src=«dopb84582.zip» v:shapes="_x0000_i1075"> и <shape id="_x0000_i1076" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image101.wmz» o:><img width=«45» height=«23» src=«dopb84583.zip» v:shapes="_x0000_i1076">
4) <shape id="_x0000_i1077" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image089.wmz» o:><img width=«80» height=«24» src=«dopb84577.zip» v:shapes="_x0000_i1077"> = -1 х = 0 или х = 1. При х = 0 <shape id="_x0000_i1078" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image103.wmz» o:><img width=«52» height=«24» src=«dopb84584.zip» v:shapes="_x0000_i1078"> = -1. (-1)-1 ≠ (-1)0. Это не решение. При х = 1 (-1)0= (-1)0. Это решение х3 = 1.
5) <shape id="_x0000_i1079" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image089.wmz» o:><img width=«80» height=«24» src=«dopb84577.zip» v:shapes="_x0000_i1079"> ≠ 0 и <shape id="_x0000_i1080" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image089.wmz» o:><img width=«80» height=«24» src=«dopb84577.zip» v:shapes="_x0000_i1080"> ≠ ±1 имеем <shape id="_x0000_i1081" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image105.wmz» o:><img width=«52» height=«24» src=«dopb84584.zip» v:shapes="_x0000_i1081"> = 0, <shape id="_x0000_i1082" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image106.wmz» o:><img width=«17» height=«16» src=«dopb84585.zip» v:shapes="_x0000_i1082"> = -1 или
<shape id="_x0000_i1083" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image108.wmz» o:><img width=«17» height=«16» src=«dopb84585.zip» v:shapes="_x0000_i1083"> = 1. Эти корни уже учтены.
Ответ: -1, 1, 2.
Пример №4.
<shape id="_x0000_i1084" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image109.wmz» o:><img width=«147» height=«41» src=«dopb84586.zip» v:shapes="_x0000_i1084">
Решение
1) При <shape id="_x0000_i1085" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image111.wmz» o:><img width=«60» height=«19» src=«dopb84587.zip» v:shapes="_x0000_i1085">решений нет, т.к. 0 в любой степени не равен 1.
при <shape id="_x0000_i1086" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image113.wmz» o:><img width=«60» height=«19» src=«dopb84588.zip» v:shapes="_x0000_i1086">, <shape id="_x0000_i1087" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image115.wmz» o:><img width=«141» height=«28» src=«dopb84589.zip» v:shapes="_x0000_i1087">
2) <shape id="_x0000_i1088" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image117.wmz» o:><img width=«57» height=«19» src=«dopb84590.zip» v:shapes="_x0000_i1088">, <shape id="_x0000_i1089" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image119.wmz» o:><img width=«44» height=«23» src=«dopb84591.zip» v:shapes="_x0000_i1089">.
3) <shape id="_x0000_i1090" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image121.wmz» o:><img width=«68» height=«19» src=«dopb84592.zip» v:shapes="_x0000_i1090">, <shape id="_x0000_i1091" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image123.wmz» o:><img width=«39» height=«19» src=«dopb84593.zip» v:shapes="_x0000_i1091">.
<shape id="_x0000_i1092" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image125.wmz» o:><img width=«92» height=«21» src=«dopb84594.zip» v:shapes="_x0000_i1092">, (-1)0 = (-1)0это решение.
<shape id="_x0000_i1093" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image127.wmz» o:><img width=«45» height=«23» src=«dopb84583.zip» v:shapes="_x0000_i1093">.
4) <shape id="_x0000_i1094" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image128.wmz» o:><img width=«60» height=«19» src=«dopb84588.zip» v:shapes="_x0000_i1094"> и <shape id="_x0000_i1095" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image129.wmz» o:><img width=«68» height=«19» src=«dopb84595.zip» v:shapes="_x0000_i1095">
<shape id="_x0000_i1096" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image125.wmz» o:><img width=«92» height=«21» src=«dopb84594.zip» v:shapes="_x0000_i1096">
<shape id="_x0000_i1097" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image131.wmz» o:><img width=«45» height=«19» src=«dopb84596.zip» v:shapes="_x0000_i1097"> или <shape id="_x0000_i1098" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image133.wmz» o:><img width=«41» height=«19» src=«dopb84597.zip» v:shapes="_x0000_i1098">
При <shape id="_x0000_i1099" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image131.wmz» o:><img width=«45» height=«19» src=«dopb84596.zip» v:shapes="_x0000_i1099"> (-4)0= 1 – верно. <shape id="_x0000_i1100" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image135.wmz» o:><img width=«65» height=«24» src=«dopb84598.zip» v:shapes="_x0000_i1100">
Ответ: -1, 2, 4.
Пример №5.
<shape id="_x0000_i1101" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image137.wmz» o:><img width=«192» height=«42» src=«dopb84599.zip» v:shapes="_x0000_i1101">
Решение
1) <shape id="_x0000_i1102" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image139.wmz» o:><img width=«65» height=«27» src=«dopb84600.zip» v:shapes="_x0000_i1102">, <shape id="_x0000_i1103" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image141.wmz» o:><img width=«39» height=«19» src=«dopb84593.zip» v:shapes="_x0000_i1103">, <shape id="_x0000_i1104" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image142.wmz» o:><img width=«77» height=«21» src=«dopb84601.zip» v:shapes="_x0000_i1104"> это не решение.
2) <shape id="_x0000_i1105" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image144.wmz» o:><img width=«63» height=«27» src=«dopb84602.zip» v:shapes="_x0000_i1105">, <shape id="_x0000_i1106" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image146.wmz» o:><img width=«43» height=«23» src=«dopb84603.zip» v:shapes="_x0000_i1106"> и <shape id="_x0000_i1107" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image148.wmz» o:><img width=«43» height=«23» src=«dopb84604.zip» v:shapes="_x0000_i1107">.
3) отрицательных значений основание не имеет. При <shape id="_x0000_i1108" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image150.wmz» o:><img width=«65» height=«27» src=«dopb84605.zip» v:shapes="_x0000_i1108"> и <shape id="_x0000_i1109" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image152.wmz» o:><img width=«63» height=«27» src=«dopb84606.zip» v:shapes="_x0000_i1109">, <shape id="_x0000_i1110" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image154.wmz» o:><img width=«115» height=«21» src=«dopb84607.zip» v:shapes="_x0000_i1110">, <shape id="_x0000_i1111" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image156.wmz» o:><img width=«107» height=«21» src=«dopb84608.zip» v:shapes="_x0000_i1111">,
х = 5, 315 = 315 – верно. х3 = 5,
х = 2 – не является решением.
Ответ: 1,3,5.
Пример №6
<shape id="_x0000_i1112" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image158.wmz» o:><img width=«87» height=«41» src=«dopb84609.zip» v:shapes="_x0000_i1112">
Решение
1) <shape id="_x0000_i1113" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image160.wmz» o:><img width=«43» height=«27» src=«dopb84610.zip» v:shapes="_x0000_i1113"> не дает решений, т.к. 0 ни в какой степени не равен 1.
2) <shape id="_x0000_i1114" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image162.wmz» o:><img width=«40» height=«27» src=«dopb84611.zip» v:shapes="_x0000_i1114">. <shape id="_x0000_i1115" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image164.wmz» o:><img width=«40» height=«23» src=«dopb84612.zip» v:shapes="_x0000_i1115"> или <shape id="_x0000_i1116" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image166.wmz» o:><img width=«53» height=«23» src=«dopb84613.zip» v:shapes="_x0000_i1116">.
3) отрицательных значений <shape id="_x0000_i1117" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image168.wmz» o:><img width=«17» height=«27» src=«dopb84614.zip» v:shapes="_x0000_i1117"> не имеет.
4) При <shape id="_x0000_i1118" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image170.wmz» o:><img width=«39» height=«19» src=«dopb84615.zip» v:shapes="_x0000_i1118">, <shape id="_x0000_i1119" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image172.wmz» o:><img width=«83» height=«32» src=«dopb84616.zip» v:shapes="_x0000_i1119">
<shape id="_x0000_i1120" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image174.wmz» o:><img width=«77» height=«21» src=«dopb84601.zip» v:shapes="_x0000_i1120">, т.к. <shape id="_x0000_i1121" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image175.wmz» o:><img width=«39» height=«19» src=«dopb84615.zip» v:shapes="_x0000_i1121">, то <shape id="_x0000_i1122" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image176.wmz» o:><img width=«39» height=«19» src=«dopb84593.zip» v:shapes="_x0000_i1122">. Проверка 20= 1 – верно. <shape id="_x0000_i1123" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image177.wmz» o:><img width=«45» height=«24» src=«dopb84617.zip» v:shapes="_x0000_i1123">
Ответ: -1, 1, 2.
Пример №7
<shape id="_x0000_i1124" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image179.wmz» o:><img width=«213» height=«42» src=«dopb84618.zip» v:shapes="_x0000_i1124">
Решение
1) <shape id="_x0000_i1125" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image181.wmz» o:><img width=«60» height=«19» src=«dopb84619.zip» v:shapes="_x0000_i1125">, <shape id="_x0000_i1126" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image183.wmz» o:><img width=«47» height=«19» src=«dopb84620.zip» v:shapes="_x0000_i1126">, <shape id="_x0000_i1127" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image185.wmz» o:><img width=«69» height=«21» src=«dopb84621.zip» v:shapes="_x0000_i1127">, <shape id="_x0000_i1128" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image187.wmz» o:><img width=«57» height=«19» src=«dopb84622.zip» v:shapes="_x0000_i1128">. Это решение <shape id="_x0000_i1129" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image189.wmz» o:><img width=«52» height=«23» src=«dopb84623.zip» v:shapes="_x0000_i1129">.
2) <shape id="_x0000_i1130" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image191.wmz» o:><img width=«57» height=«19» src=«dopb84624.zip» v:shapes="_x0000_i1130">, <shape id="_x0000_i1131" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image193.wmz» o:><img width=«55» height=«23» src=«dopb84625.zip» v:shapes="_x0000_i1131">.
3) <shape id="_x0000_i1132" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image195.wmz» o:><img width=«68» height=«19» src=«dopb84626.zip» v:shapes="_x0000_i1132">, <shape id="_x0000_i1133" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image197.wmz» o:><img width=«47» height=«15» src=«dopb84627.zip» v:shapes="_x0000_i1133">, <shape id="_x0000_i1134" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image199.wmz» o:><img width=«43» height=«21» src=«dopb84628.zip» v:shapes="_x0000_i1134"> - четное и -3х – четное. Это решение. х2 = -4.
4) <shape id="_x0000_i1135" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image201.wmz» o:><img width=«60» height=«19» src=«dopb84629.zip» v:shapes="_x0000_i1135"> и <shape id="_x0000_i1136" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image203.wmz» o:><img width=«68» height=«19» src=«dopb84630.zip» v:shapes="_x0000_i1136">, <shape id="_x0000_i1137" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image205.wmz» o:><img width=«87» height=«21» src=«dopb84631.zip» v:shapes="_x0000_i1137">, <shape id="_x0000_i1138" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image207.wmz» o:><img width=«100» height=«21» src=«dopb84632.zip» v:shapes="_x0000_i1138">, <shape id="_x0000_i1139" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image209.wmz» o:><img width=«35» height=«19» src=«dopb84633.zip» v:shapes="_x0000_i1139">, 4-3 = 4-3 – верно. <shape id="_x0000_i1140" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image211.wmz» o:><img width=«41» height=«24» src=«dopb84634.zip» v:shapes="_x0000_i1140">.
Ответ: -4, -3, -2, 1
Пример №8
<shape id="_x0000_i1141" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image213.wmz» o:><img width=«199» height=«47» src=«dopb84635.zip» v:shapes="_x0000_i1141">
Решение
ОДЗ: <shape id="_x0000_i1142" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image215.wmz» o:><img width=«88» height=«21» src=«dopb84636.zip» v:shapes="_x0000_i1142">, <shape id="_x0000_i1143" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image217.wmz» o:><img width=«77» height=«21» src=«dopb84637.zip» v:shapes="_x0000_i1143">
<shape id="_x0000_i1144" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image219.wmz» o:><img width=«105» height=«19» src=«dopb84638.zip» v:shapes="_x0000_i1144">, <shape id="_x0000_i1145" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image221.wmz» o:><img width=«89» height=«27» src=«dopb84639.zip» v:shapes="_x0000_i1145">,
<shape id="_x0000_i1146" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image223.wmz» o:><img width=«65» height=«27» src=«dopb84640.zip» v:shapes="_x0000_i1146"> и <shape id="_x0000_i1147" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image225.wmz» o:><img width=«73» height=«27» src=«dopb84641.zip» v:shapes="_x0000_i1147">
<shape id="_x0000_i1148" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image227.wmz» o:><img width=«73» height=«19» src=«dopb84642.zip» v:shapes="_x0000_i1148">
Все решения принадлежат уравнению <shape id="_x0000_i1149" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image229.wmz» o:><img width=«76» height=«25» src=«dopb84643.zip» v:shapes="_x0000_i1149">=2.
<shape id="_x0000_i1150" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image231.wmz» o:><img width=«89» height=«21» src=«dopb84644.zip» v:shapes="_x0000_i1150">, <shape id="_x0000_i1151" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image233.wmz» o:><img width=«100» height=«21» src=«dopb84645.zip» v:shapes="_x0000_i1151">, <shape id="_x0000_i1152" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image235.wmz» o:><img width=«45» height=«19» src=«dopb84596.zip» v:shapes="_x0000_i1152"> и <shape id="_x0000_i1153" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image236.wmz» o:><img width=«47» height=«19» src=«dopb84646.zip» v:shapes="_x0000_i1153">. Оба значения принадлежат к ОДЗ.
Ответ: -4, -1.
Пример №9
<shape id="_x0000_i1154" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image238.wmz» o:><img width=«167» height=«49» src=«dopb84647.zip» v:shapes="_x0000_i1154">
Решение
ОДЗ: <shape id="_x0000_i1155" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image240.wmz» o:><img width=«84» height=«21» src=«dopb84648.zip» v:shapes="_x0000_i1155">, <shape id="_x0000_i1156" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image242.wmz» o:><img width=«37» height=«19» src=«dopb84649.zip» v:shapes="_x0000_i1156">, <shape id="_x0000_i1157" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image244.wmz» o:><img width=«40» height=«41» src=«dopb84650.zip» v:shapes="_x0000_i1157">.
1) <shape id="_x0000_i1158" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image246.wmz» o:><img width=«73» height=«27» src=«dopb84651.zip» v:shapes="_x0000_i1158"> решений не имеет, т.к. 0 в любой степени не равен 1.
При <shape id="_x0000_i1159" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image248.wmz» o:><img width=«73» height=«27» src=«dopb84652.zip» v:shapes="_x0000_i1159">, <shape id="_x0000_i1160" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image250.wmz» o:><img width=«65» height=«19» src=«dopb84653.zip» v:shapes="_x0000_i1160"> или <shape id="_x0000_i1161" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image252.wmz» o:><img width=«76» height=«19» src=«dopb84654.zip» v:shapes="_x0000_i1161">,
<shape id="_x0000_i1162" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image254.wmz» o:><img width=«48» height=«19» src=«dopb84655.zip» v:shapes="_x0000_i1162">ОДЗ, <shape id="_x0000_i1163" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image256.wmz» o:><img width=«57» height=«19» src=«dopb84656.zip» v:shapes="_x0000_i1163">ОДЗ.
Значит все решения содержатся в уровнении <shape id="_x0000_i1164" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image258.wmz» o:><img width=«64» height=«25» src=«dopb84657.zip» v:shapes="_x0000_i1164">= 0, <shape id="_x0000_i1165" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image260.wmz» o:><img width=«37» height=«19» src=«dopb84658.zip» v:shapes="_x0000_i1165"> или <shape id="_x0000_i1166" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image262.wmz» o:><img width=«41» height=«41» src=«dopb84659.zip» v:shapes="_x0000_i1166">.
Проверка: <shape id="_x0000_i1167" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image264.wmz» o:><img width=«37» height=«19» src=«dopb84658.zip» v:shapes="_x0000_i1167">, 20= 1 – верно.
<shape id="_x0000_i1168" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image265.wmz» o:><img width=«41» height=«41» src=«dopb84659.zip» v:shapes="_x0000_i1168">, <shape id="_x0000_i1169" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image266.wmz» o:><img width=«60» height=«49» src=«dopb84660.zip» v:shapes="_x0000_i1169"> - верно.
Ответ: 0, 3/2.
Пример №10
<shape id="_x0000_i1170" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image268.wmz» o:><img width=«180» height=«53» src=«dopb84661.zip» v:shapes="_x0000_i1170">
Решение
1) <shape id="_x0000_i1171" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image270.wmz» o:><img width=«64» height=«27» src=«dopb84662.zip» v:shapes="_x0000_i1171"> решений не дает, т.к. 0 в любой степени не равен 1.
2) При <shape id="_x0000_i1172" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image272.wmz» o:><img width=«65» height=«27» src=«dopb84663.zip» v:shapes="_x0000_i1172">, <shape id="_x0000_i1173" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image274.wmz» o:><img width=«145» height=«32» src=«dopb84664.zip» v:shapes="_x0000_i1173">, <shape id="_x0000_i1174" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image276.wmz» o:><img width=«65» height=«27» src=«dopb84665.zip» v:shapes="_x0000_i1174">. Все решения принадлежат уравнению <shape id="_x0000_i1175" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image278.wmz» o:><img width=«113» height=«21» src=«dopb84666.zip» v:shapes="_x0000_i1175">. <shape id="_x0000_i1176" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image280.wmz» o:><img width=«40» height=«41» src=«dopb84667.zip» v:shapes="_x0000_i1176"> или <shape id="_x0000_i1177" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image282.wmz» o:><img width=«37» height=«19» src=«dopb84668.zip» v:shapes="_x0000_i1177">.
3) <shape id="_x0000_i1178" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image284.wmz» o:><img width=«61» height=«27» src=«dopb84669.zip» v:shapes="_x0000_i1178">, <shape id="_x0000_i1179" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image286.wmz» o:><img width=«44» height=«23» src=«dopb84591.zip» v:shapes="_x0000_i1179"> и <shape id="_x0000_i1180" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image287.wmz» o:><img width=«45» height=«23» src=«dopb84583.zip» v:shapes="_x0000_i1180">.
Второе решение не подходит, т.к <shape id="_x0000_i1181" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image282.wmz» o:><img width=«37» height=«19» src=«dopb84668.zip» v:shapes="_x0000_i1181">, <shape id="_x0000_i1182" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image288.wmz» o:><img width=«64» height=«27» src=«dopb84662.zip» v:shapes="_x0000_i1182">. А <shape id="_x0000_i1183" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image289.wmz» o:><img width=«40» height=«41» src=«dopb84667.zip» v:shapes="_x0000_i1183"> является решением <shape id="_x0000_i1184" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image290.wmz» o:><img width=«85» height=«49» src=«dopb84670.zip» v:shapes="_x0000_i1184">
Ответ: <shape id="_x0000_i1185" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image292.wmz» o:><img width=«15» height=«41» src=«dopb84671.zip» v:shapes="_x0000_i1185">, 2, 4.
Пример №11
<shape id="_x0000_i1186" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image294.wmz» o:><img width=«194» height=«34» src=«dopb84672.zip» v:shapes="_x0000_i1186">
Решение
1) <shape id="_x0000_i1187" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image296.wmz» o:><img width=«61» height=«19» src=«dopb84673.zip» v:shapes="_x0000_i1187">, <shape id="_x0000_i1188" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image298.wmz» o:><img width=«47» height=«19» src=«dopb84674.zip» v:shapes="_x0000_i1188">, <shape id="_x0000_i1189" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image300.wmz» o:><img width=«87» height=«21» src=«dopb84675.zip» v:shapes="_x0000_i1189"> и <shape id="_x0000_i1190" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image302.wmz» o:><img width=«65» height=«19» src=«dopb84676.zip» v:shapes="_x0000_i1190"> это решение <shape id="_x0000_i1191" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image304.wmz» o:><img width=«52» height=«23» src=«dopb84677.zip» v:shapes="_x0000_i1191">.
2) <shape id="_x0000_i1192" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image306.wmz» o:><img width=«59» height=«19» src=«dopb84678.zip» v:shapes="_x0000_i1192">, <shape id="_x0000_i1193" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image308.wmz» o:><img width=«53» height=«23» src=«dopb84613.zip» v:shapes="_x0000_i1193">.
3) <shape id="_x0000_i1194" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image309.wmz» o:><img width=«69» height=«19» src=«dopb84679.zip» v:shapes="_x0000_i1194">, <shape id="_x0000_i1195" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image311.wmz» o:><img width=«47» height=«19» src=«dopb84620.zip» v:shapes="_x0000_i1195">, <shape id="_x0000_i1196" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image312.wmz» o:><img width=«60» height=«21» src=«dopb84680.zip» v:shapes="_x0000_i1196"> - четное, <shape id="_x0000_i1197" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image314.wmz» o:><img width=«40» height=«19» src=«dopb84681.zip» v:shapes="_x0000_i1197"> - нечетное. Это является решением.
4) <shape id="_x0000_i1198" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image316.wmz» o:><img width=«60» height=«19» src=«dopb84619.zip» v:shapes="_x0000_i1198"> или <shape id="_x0000_i1199" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image317.wmz» o:><img width=«68» height=«19» src=«dopb84630.zip» v:shapes="_x0000_i1199">, <shape id="_x0000_i1200" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image318.wmz» o:><img width=«111» height=«21» src=«dopb84682.zip» v:shapes="_x0000_i1200">, <shape id="_x0000_i1201" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image320.wmz» o:><img width=«123» height=«21» src=«dopb84683.zip» v:shapes="_x0000_i1201">, <shape id="_x0000_i1202" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image322.wmz» o:><img width=«47» height=«19» src=«dopb84646.zip» v:shapes="_x0000_i1202">, <shape id="_x0000_i1203" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image323.wmz» o:><img width=«59» height=«19» src=«dopb84684.zip» v:shapes="_x0000_i1203">.
Проверка: <shape id="_x0000_i1204" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image325.wmz» o:><img width=«47» height=«19» src=«dopb84646.zip» v:shapes="_x0000_i1204">, <shape id="_x0000_i1205" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image326.wmz» o:><img width=«104» height=«25» src=«dopb84685.zip» v:shapes="_x0000_i1205"> - верно.
Но <shape id="_x0000_i1206" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image328.wmz» o:><img width=«59» height=«19» src=«dopb84684.zip» v:shapes="_x0000_i1206"> не является корнем!
Выражение (-1,5)52,5, которое получается при проверке не имеет смысла, т.к. степень отрицательно числа имеет смысл только для целых показателей. Равенство <shape id="_x0000_i1207" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image329.wmz» o:><img width=«23» height=«33» src=«dopb84686.zip» v:shapes="_x0000_i1207">= <shape id="_x0000_i1208" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image331.wmz» o:><img width=«44» height=«29» src=«dopb84687.zip» v:shapes="_x0000_i1208"> только для <shape id="_x0000_i1209" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image333.wmz» o:><img width=«37» height=«19» src=«dopb84688.zip» v:shapes="_x0000_i1209">. Значит, отрицательное число можно возводить только в степень с целым показателем.
Ответ: -4, -2, -1.
Пример №12
<shape id="_x0000_i1210" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image335.wmz» o:><img width=«139» height=«40» src=«dopb84689.zip» v:shapes="_x0000_i1210">
Решение
ОДЗ: <shape id="_x0000_i1211" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image337.wmz» o:><img width=«39» height=«19» src=«dopb84690.zip» v:shapes="_x0000_i1211">. Значит 0,1 и -1 отпадают.
<shape id="_x0000_i1212" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image339.wmz» o:><img width=«180» height=«41» src=«dopb84691.zip» v:shapes="_x0000_i1212"> и все решения содержатся в уравнении.
<shape id="_x0000_i1213" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image341.wmz» o:><img width=«133» height=«25» src=«dopb84692.zip» v:shapes="_x0000_i1213">
<shape id="_x0000_i1214" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image343.wmz» o:><img width=«100» height=«25» src=«dopb84693.zip» v:shapes="_x0000_i1214">, <shape id="_x0000_i1215" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image345.wmz» o:><img width=«60» height=«19» src=«dopb84694.zip» v:shapes="_x0000_i1215">, <shape id="_x0000_i1216" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image347.wmz» o:><img width=«84» height=«21» src=«dopb84695.zip» v:shapes="_x0000_i1216">
Ответ: 5.
Пример №13
<shape id="_x0000_i1217" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image349.wmz» o:><img width=«158» height=«40» src=«dopb84696.zip» v:shapes="_x0000_i1217">
Решение
<shape id="_x0000_i1218" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image351.wmz» o:><img width=«121» height=«32» src=«dopb84697.zip» v:shapes="_x0000_i1218">
1) <shape id="_x0000_i1219" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image353.wmz» o:><img width=«64» height=«27» src=«dopb84662.zip» v:shapes="_x0000_i1219">, <shape id="_x0000_i1220" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image354.wmz» o:><img width=«37» height=«19» src=«dopb84668.zip» v:shapes="_x0000_i1220">, <shape id="_x0000_i1221" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image355.wmz» o:><img width=«71» height=«21» src=«dopb84698.zip» v:shapes="_x0000_i1221">. Это решение <shape id="_x0000_i1222" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image357.wmz» o:><img width=«43» height=«23» src=«dopb84603.zip» v:shapes="_x0000_i1222">.
2) <shape id="_x0000_i1223" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image358.wmz» o:><img width=«61» height=«27» src=«dopb84669.zip» v:shapes="_x0000_i1223">, <shape id="_x0000_i1224" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image359.wmz» o:><img width=«45» height=«23» src=«dopb84699.zip» v:shapes="_x0000_i1224">, <shape id="_x0000_i1225" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image361.wmz» o:><img width=«45» height=«23» src=«dopb84583.zip» v:shapes="_x0000_i1225">.
3) отрицательных значений <shape id="_x0000_i1226" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image362.wmz» o:><img width=«40» height=«27» src=«dopb84700.zip» v:shapes="_x0000_i1226"> не имеет.
При <shape id="_x0000_i1227" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image353.wmz» o:><img width=«64» height=«27» src=«dopb84662.zip» v:shapes="_x0000_i1227"> или <shape id="_x0000_i1228" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image364.wmz» o:><img width=«72» height=«27» src=«dopb84701.zip» v:shapes="_x0000_i1228"> все решения в уравнении <shape id="_x0000_i1229" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image366.wmz» o:><img width=«69» height=«21» src=«dopb84702.zip» v:shapes="_x0000_i1229">, <shape id="_x0000_i1230" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image368.wmz» o:><img width=«39» height=«19» src=«dopb84593.zip» v:shapes="_x0000_i1230"> и <shape id="_x0000_i1231" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image369.wmz» o:><img width=«45» height=«19» src=«dopb84596.zip» v:shapes="_x0000_i1231">.
При <shape id="_x0000_i1232" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image370.wmz» o:><img width=«45» height=«19» src=«dopb84596.zip» v:shapes="_x0000_i1232">, <shape id="_x0000_i1233" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image371.wmz» o:><img width=«52» height=«20» src=«dopb84703.zip» v:shapes="_x0000_i1233"> - верно. <shape id="_x0000_i1234" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image373.wmz» o:><img width=«53» height=«23» src=«dopb84704.zip» v:shapes="_x0000_i1234">.
Ответ: -1, 2, 3, 4.
Пример №14
<shape id="_x0000_i1235" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image375.wmz» o:><img width=«146» height=«51» src=«dopb84705.zip» v:shapes="_x0000_i1235">
Решение
ОДЗ: <shape id="_x0000_i1236" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image377.wmz» o:><img width=«39» height=«19» src=«dopb84706.zip» v:shapes="_x0000_i1236">
1) При <shape id="_x0000_i1237" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image379.wmz» o:><img width=«64» height=«27» src=«dopb84662.zip» v:shapes="_x0000_i1237"> решений нет, т.к. 0 в любой степени не равен 1.
При <shape id="_x0000_i1238" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image380.wmz» o:><img width=«65» height=«27» src=«dopb84663.zip» v:shapes="_x0000_i1238">
<shape id="_x0000_i1239" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image381.wmz» o:><img width=«186» height=«51» src=«dopb84707.zip» v:shapes="_x0000_i1239">
2) <shape id="_x0000_i1240" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image383.wmz» o:><img width=«61» height=«27» src=«dopb84669.zip» v:shapes="_x0000_i1240">, <shape id="_x0000_i1241" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image384.wmz» o:><img width=«39» height=«19» src=«dopb84708.zip» v:shapes="_x0000_i1241">и <shape id="_x0000_i1242" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image386.wmz» o:><img width=«39» height=«19» src=«dopb84593.zip» v:shapes="_x0000_i1242">. <shape id="_x0000_i1243" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image387.wmz» o:><img width=«44» height=«23» src=«dopb84591.zip» v:shapes="_x0000_i1243"> — решение, а <shape id="_x0000_i1244" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image388.wmz» o:><img width=«84» height=«21» src=«dopb84709.zip» v:shapes="_x0000_i1244">.
3) <shape id="_x0000_i1245" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image390.wmz» o:><img width=«64» height=«27» src=«dopb84710.zip» v:shapes="_x0000_i1245"> для всех <shape id="_x0000_i1246" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image106.wmz» o:><img width=«13» height=«15» src=«dopb84711.zip» v:shapes="_x0000_i1246">. При <shape id="_x0000_i1247" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image393.wmz» o:><img width=«65» height=«27» src=«dopb84663.zip» v:shapes="_x0000_i1247"> и <shape id="_x0000_i1248" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image394.wmz» o:><img width=«61» height=«27» src=«dopb84712.zip» v:shapes="_x0000_i1248"> все решения содержатся в уравнении <shape id="_x0000_i1249" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image396.wmz» o:><img width=«108» height=«44» src=«dopb84713.zip» v:shapes="_x0000_i1249">, <shape id="_x0000_i1250" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image398.wmz» o:><img width=«37» height=«19» src=«dopb84714.zip» v:shapes="_x0000_i1250"> или <shape id="_x0000_i1251" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image400.wmz» o:><img width=«37» height=«19» src=«dopb84668.zip» v:shapes="_x0000_i1251">. При <shape id="_x0000_i1252" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image401.wmz» o:><img width=«37» height=«19» src=«dopb84668.zip» v:shapes="_x0000_i1252"> , <shape id="_x0000_i1253" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image402.wmz» o:><img width=«64» height=«27» src=«dopb84662.zip» v:shapes="_x0000_i1253">.
При <shape id="_x0000_i1254" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image403.wmz» o:><img width=«37» height=«19» src=«dopb84714.zip» v:shapes="_x0000_i1254">, <shape id="_x0000_i1255" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image404.wmz» o:><img width=«52» height=«20» src=«dopb84715.zip» v:shapes="_x0000_i1255"> - верно. <shape id="_x0000_i1256" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image406.wmz» o:><img width=«44» height=«23» src=«dopb84716.zip» v:shapes="_x0000_i1256">.
Ответ: 4, 5.
Пример №15.
<shape id="_x0000_i1257" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image408.wmz» o:><img width=«199» height=«53» src=«dopb84717.zip» v:shapes="_x0000_i1257">, <shape id="_x0000_i1258" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image410.wmz» o:><img width=«58» height=«28» src=«dopb84718.zip» v:shapes="_x0000_i1258">
Решение
<shape id="_x0000_i1259" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image412.wmz» o:><img width=«9» height=«20» src=«dopb84719.zip» v:shapes="_x0000_i1259"><shape id="_x0000_i1260" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image414.wmz» o:><img width=«132» height=«88» src=«dopb84720.zip» v:shapes="_x0000_i1260">
используя свойства логарифма <shape id="_x0000_i1261" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image416.wmz» o:><img width=«84» height=«29» src=«dopb84721.zip» v:shapes="_x0000_i1261"> и <shape id="_x0000_i1262" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image418.wmz» o:><img width=«126» height=«34» src=«dopb84722.zip» v:shapes="_x0000_i1262">получили:
<shape id="_x0000_i1263" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image420.wmz» o:><img width=«236» height=«50» src=«dopb84723.zip» v:shapes="_x0000_i1263">= <shape id="_x0000_i1264" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image422.wmz» o:><img width=«182» height=«37» src=«dopb84724.zip» v:shapes="_x0000_i1264">
В первой части уравнения выполнили преобразования
<shape id="_x0000_i1265" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image424.wmz» o:><img width=«166» height=«31» src=«dopb84725.zip» v:shapes="_x0000_i1265">. Получили уравнение <shape id="_x0000_i1266" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image426.wmz» o:><img width=«69» height=«21» src=«dopb84702.zip» v:shapes="_x0000_i1266">. Все решения содержатся в уравнении.
<shape id="_x0000_i1267" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image427.wmz» o:><img width=«39» height=«19» src=«dopb84593.zip» v:shapes="_x0000_i1267"> или <shape id="_x0000_i1268" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image428.wmz» o:><img width=«45» height=«19» src=«dopb84596.zip» v:shapes="_x0000_i1268">. <shape id="_x0000_i1269" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image429.wmz» o:><img width=«68» height=«21» src=«dopb84726.zip» v:shapes="_x0000_i1269">
Ответ: 2.
Пример №16
<shape id="_x0000_i1270" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image431.wmz» o:><img width=«367» height=«93» src=«dopb84727.zip» v:shapes="_x0000_i1270">
Решение
ОДЗ: <shape id="_x0000_i1271" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image433.wmz» o:><img width=«39» height=«19» src=«dopb84728.zip» v:shapes="_x0000_i1271">
Преобразуем знаменатель дроби в правой части уравнения
<shape id="_x0000_i1272" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image435.wmz» o:><img width=«331» height=«51» src=«dopb84729.zip» v:shapes="_x0000_i1272">; <shape id="_x0000_i1273" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image437.wmz» o:><img width=«107» height=«41» src=«dopb84730.zip» v:shapes="_x0000_i1273">.
<shape id="_x0000_i1274" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image439.wmz» o:><img width=«123» height=«34» src=«dopb84731.zip» v:shapes="_x0000_i1274">, <shape id="_x0000_i1275" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image441.wmz» o:><img width=«125» height=«34» src=«dopb84732.zip» v:shapes="_x0000_i1275">, где <shape id="_x0000_i1276" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image443.wmz» o:><img width=«39» height=«19» src=«dopb84728.zip» v:shapes="_x0000_i1276">
1) <shape id="_x0000_i1277" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image444.wmz» o:><img width=«35» height=«19» src=«dopb84633.zip» v:shapes="_x0000_i1277">, <shape id="_x0000_i1278" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image445.wmz» o:><img width=«40» height=«20» src=«dopb84733.zip» v:shapes="_x0000_i1278"> - верно.
2) <shape id="_x0000_i1279" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image447.wmz» o:><img width=«36» height=«19» src=«dopb84734.zip» v:shapes="_x0000_i1279">, <shape id="_x0000_i1280" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image449.wmz» o:><img width=«119» height=«24» src=«dopb84735.zip» v:shapes="_x0000_i1280">
Пасть <shape id="_x0000_i1281" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image451.wmz» o:><img width=«51» height=«21» src=«dopb84736.zip» v:shapes="_x0000_i1281">, тогда <shape id="_x0000_i1282" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image453.wmz» o:><img width=«103» height=«24» src=«dopb84737.zip» v:shapes="_x0000_i1282">
<shape id="_x0000_i1283" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image455.wmz» o:><img width=«133» height=«24» src=«dopb84738.zip» v:shapes="_x0000_i1283">
<shape id="_x0000_i1284" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image457.wmz» o:><img width=«73» height=«41» src=«dopb84739.zip» v:shapes="_x0000_i1284">, <shape id="_x0000_i1285" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image459.wmz» o:><img width=«53» height=«23» src=«dopb84740.zip» v:shapes="_x0000_i1285"> или <shape id="_x0000_i1286" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image461.wmz» o:><img width=«13» height=«25» src=«dopb84741.zip» v:shapes="_x0000_i1286"><shape id="_x0000_i1287" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image463.wmz» o:><img width=«53» height=«23» src=«dopb84742.zip» v:shapes="_x0000_i1287">.
Следовательно; <shape id="_x0000_i1288" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image465.wmz» o:><img width=«59» height=«21» src=«dopb84743.zip» v:shapes="_x0000_i1288"> или <shape id="_x0000_i1289" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image467.wmz» o:><img width=«155» height=«24» src=«dopb84744.zip» v:shapes="_x0000_i1289">, <shape id="_x0000_i1290" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image469.wmz» o:><img width=«57» height=«21» src=«dopb84745.zip» v:shapes="_x0000_i1290">, <shape id="_x0000_i1291" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image471.wmz» o:><img width=«101» height=«24» src=«dopb84746.zip» v:shapes="_x0000_i1291">.
Ответ: 1, 0,1, 0, 0,01.
Пример №17
<shape id="_x0000_i1292" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image473.wmz» o:><img width=«231» height=«38» src=«dopb84747.zip» v:shapes="_x0000_i1292">
Решение
ОДЗ: <shape id="_x0000_i1293" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image475.wmz» o:><img width=«39» height=«19» src=«dopb84728.zip» v:shapes="_x0000_i1293"> и <shape id="_x0000_i1294" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image476.wmz» o:><img width=«36» height=«19» src=«dopb84734.zip» v:shapes="_x0000_i1294">
Выполним преобразования.
<shape id="_x0000_i1295" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image477.wmz» o:><img width=«43» height=«23» src=«dopb84748.zip» v:shapes="_x0000_i1295">+<shape id="_x0000_i1296" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image479.wmz» o:><img width=«44» height=«24» src=«dopb84749.zip» v:shapes="_x0000_i1296">= 2+2
<shape id="_x0000_i1297" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image477.wmz» o:><img width=«43» height=«23» src=«dopb84748.zip» v:shapes="_x0000_i1297">+<shape id="_x0000_i1298" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image481.wmz» o:><img width=«44» height=«36» src=«dopb84750.zip» v:shapes="_x0000_i1298">= 4
Пусть <shape id="_x0000_i1299" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image483.wmz» o:><img width=«75» height=«27» src=«dopb84751.zip» v:shapes="_x0000_i1299">, а <shape id="_x0000_i1300" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image485.wmz» o:><img width=«68» height=«24» src=«dopb84752.zip» v:shapes="_x0000_i1300">, <shape id="_x0000_i1301" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image487.wmz» o:><img width=«48» height=«24» src=«dopb84753.zip» v:shapes="_x0000_i1301">
Следовательно, <shape id="_x0000_i1302" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image489.wmz» o:><img width=«79» height=«49» src=«dopb84754.zip» v:shapes="_x0000_i1302"> или
<shape id="_x0000_i1303" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image491.wmz» o:><img width=«71» height=«20» src=«dopb84755.zip» v:shapes="_x0000_i1303">, <shape id="_x0000_i1304" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image493.wmz» o:><img width=«72» height=«27» src=«dopb84756.zip» v:shapes="_x0000_i1304">
2*2t = 4 <shape id="_x0000_i1305" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image495.wmz» o:><img width=«60» height=«23» src=«dopb84757.zip» v:shapes="_x0000_i1305">
2t = 4/2 <shape id="_x0000_i1306" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image497.wmz» o:><img width=«83» height=«21» src=«dopb84758.zip» v:shapes="_x0000_i1306">
2t = 2
t = 1
Ответ: 2.
Пример №18
<shape id="_x0000_i1307" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image499.wmz» o:><img width=«120» height=«68» src=«dopb84759.zip» v:shapes="_x0000_i1307">
Решение
ОДЗ: <shape id="_x0000_i1308" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image501.wmz» o:><img width=«39» height=«19» src=«dopb84728.zip» v:shapes="_x0000_i1308">
<shape id="_x0000_i1309" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image502.wmz» o:><img width=«125» height=«87» src=«dopb84760.zip» v:shapes="_x0000_i1309">; <shape id="_x0000_i1310" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image504.wmz» o:><img width=«232» height=«56» src=«dopb84761.zip» v:shapes="_x0000_i1310">
Прологарифмируем обе части равенства:
<shape id="_x0000_i1311" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image506.wmz» o:><img width=«179» height=«45» src=«dopb84762.zip» v:shapes="_x0000_i1311">
<shape id="_x0000_i1312" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image508.wmz» o:><img width=«147» height=«41» src=«dopb84763.zip» v:shapes="_x0000_i1312">, где <shape id="_x0000_i1313" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image510.wmz» o:><img width=«53» height=«21» src=«dopb84764.zip» v:shapes="_x0000_i1313">.
Умножим обе части уравнения на 2.
<shape id="_x0000_i1314" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image512.wmz» o:><img width=«136» height=«24» src=«dopb84765.zip» v:shapes="_x0000_i1314">
Пусть <shape id="_x0000_i1315" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image514.wmz» o:><img width=«51» height=«21» src=«dopb84736.zip» v:shapes="_x0000_i1315">, тогда <shape id="_x0000_i1316" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image515.wmz» o:><img width=«65» height=«24» src=«dopb84766.zip» v:shapes="_x0000_i1316">
<shape id="_x0000_i1317" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image517.wmz» o:><img width=«107» height=«24» src=«dopb84767.zip» v:shapes="_x0000_i1317">
<shape id="_x0000_i1318" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image519.wmz» o:><img width=«187» height=«25» src=«dopb84768.zip» v:shapes="_x0000_i1318">
<shape id="_x0000_i1319" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image521.wmz» o:><img width=«64» height=«41» src=«dopb84769.zip» v:shapes="_x0000_i1319">, <shape id="_x0000_i1320" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image523.wmz» o:><img width=«59» height=«41» src=«dopb84770.zip» v:shapes="_x0000_i1320"> или <shape id="_x0000_i1321" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image525.wmz» o:><img width=«44» height=«23» src=«dopb84771.zip» v:shapes="_x0000_i1321">
1) <shape id="_x0000_i1322" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image527.wmz» o:><img width=«55» height=«24» src=«dopb84772.zip» v:shapes="_x0000_i1322">, <shape id="_x0000_i1323" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image529.wmz» o:><img width=«61» height=«27» src=«dopb84773.zip» v:shapes="_x0000_i1323">
<shape id="_x0000_i1324" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image531.wmz» o:><img width=«47» height=«21» src=«dopb84774.zip» v:shapes="_x0000_i1324"> или <shape id="_x0000_i1325" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image533.wmz» o:><img width=«57» height=«21» src=«dopb84745.zip» v:shapes="_x0000_i1325">
<shape id="_x0000_i1326" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image534.wmz» o:><img width=«49» height=«23» src=«dopb84775.zip» v:shapes="_x0000_i1326"> <shape id="_x0000_i1327" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image536.wmz» o:><img width=«100» height=«24» src=«dopb84776.zip» v:shapes="_x0000_i1327">
Ответ: 0.1, 10.
Пример №19
<shape id="_x0000_i1328" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image538.wmz» o:><img width=«147» height=«43» src=«dopb84777.zip» v:shapes="_x0000_i1328">
Решение
ОДЗ: <shape id="_x0000_i1329" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image540.wmz» o:><img width=«115» height=«51» src=«dopb84778.zip» v:shapes="_x0000_i1329"><shape id="_x0000_i1330" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image542.wmz» o:><img width=«151» height=«93» src=«dopb84779.zip» v:shapes="_x0000_i1330">
Обратите внимание <shape id="_x0000_i1331" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image544.wmz» o:><img width=«39» height=«19» src=«dopb84728.zip» v:shapes="_x0000_i1331"> ниоткуда не следует! Наоборот, из ОДЗ видно, что <shape id="_x0000_i1332" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image108.wmz» o:><img width=«13» height=«15» src=«dopb84711.zip» v:shapes="_x0000_i1332">может быть отрицательным!
<shape id="_x0000_i1333" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image545.wmz» o:><img width=«153» height=«55» src=«dopb84780.zip» v:shapes="_x0000_i1333">
<shape id="_x0000_i1334" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image547.wmz» o:><img width=«119» height=«29» src=«dopb84781.zip» v:shapes="_x0000_i1334">, <shape id="_x0000_i1335" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image549.wmz» o:><img width=«84» height=«21» src=«dopb84782.zip» v:shapes="_x0000_i1335">
<shape id="_x0000_i1336" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image551.wmz» o:><img width=«37» height=«19» src=«dopb84668.zip» v:shapes="_x0000_i1336"> или <shape id="_x0000_i1337" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image552.wmz» o:><img width=«47» height=«19» src=«dopb84620.zip» v:shapes="_x0000_i1337">
Оба значения в ОДЗ.
Так как возводили в квадрат, корни надо проверить.
<shape id="_x0000_i1338" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image551.wmz» o:><img width=«37» height=«19» src=«dopb84668.zip» v:shapes="_x0000_i1338">, <shape id="_x0000_i1339" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image553.wmz» o:><img width=«131» height=«28» src=«dopb84783.zip» v:shapes="_x0000_i1339"> - верно.
<shape id="_x0000_i1340" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image555.wmz» o:><img width=«47» height=«19» src=«dopb84620.zip» v:shapes="_x0000_i1340">, <shape id="_x0000_i1341" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image556.wmz» o:><img width=«211» height=«25» src=«dopb84784.zip» v:shapes="_x0000_i1341"> - верно.
Ответ: -3, 3.
Пример №20
<shape id="_x0000_i1342" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image558.wmz» o:><img width=«120» height=«41» src=«dopb84785.zip» v:shapes="_x0000_i1342">
ОДЗ: <shape id="_x0000_i1343" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image560.wmz» o:><img width=«39» height=«19» src=«dopb84728.zip» v:shapes="_x0000_i1343">
Возведем обе части уравнения в квадрат (т.к. они положительны, то посторонние корни не появляются)
<shape id="_x0000_i1344" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image561.wmz» o:><img width=«76» height=«23» src=«dopb84786.zip» v:shapes="_x0000_i1344"> или <shape id="_x0000_i1345" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image563.wmz» o:><img width=«87» height=«41» src=«dopb84787.zip» v:shapes="_x0000_i1345">
Прологарифмируем по основанию 10.
<shape id="_x0000_i1346" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image565.wmz» o:><img width=«121» height=«41» src=«dopb84788.zip» v:shapes="_x0000_i1346">
<imagedata src=«18604.files/image567.wmz» o:><img width=«63» height=«41» src=«dopb84789.zip» v:shapes="_x0000_i1347"> или <shape id="_x0000_i1348" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image569.wmz» o:><img width=«57» height=«24» src=«dopb84790.zip» v:shapes="_x0000_i1348">
1) <shape id="_x0000_i1349" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image571.wmz» o:><img width=«67» height=«24» src=«dopb84791.zip» v:shapes="_x0000_i1349"> или <shape id="_x0000_i1350" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image573.wmz» o:><img width=«49» height=«21» src=«dopb84792.zip» v:shapes="_x0000_i1350">
<shape id="_x0000_i1351" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image575.wmz» o:><img width=«107» height=«24» src=«dopb84793.zip» v:shapes="_x0000_i1351">, <shape id="_x0000_i1352" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image577.wmz» o:><img width=«99» height=«24» src=«dopb84794.zip» v:shapes="_x0000_i1352">
Ответ: 0.01, 100.
Пример №21
<shape id="_x0000_i1353" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image579.wmz» o:><img width=«153» height=«54» src=«dopb84795.zip» v:shapes="_x0000_i1353">
Решение
ОДЗ: <shape id="_x0000_i1354" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image581.wmz» o:><img width=«39» height=«19» src=«dopb84728.zip» v:shapes="_x0000_i1354">
Прологарифмируем по основанию 10.
<shape id="_x0000_i1355" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image582.wmz» o:><img width=«188» height=«41» src=«dopb84796.zip» v:shapes="_x0000_i1355">, где <shape id="_x0000_i1356" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image584.wmz» o:><img width=«53» height=«21» src=«dopb84764.zip» v:shapes="_x0000_i1356">.
<shape id="_x0000_i1357" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image585.wmz» o:><img width=«159» height=«41» src=«dopb84797.zip» v:shapes="_x0000_i1357">
Пусть <shape id="_x0000_i1358" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image587.wmz» o:><img width=«47» height=«21» src=«dopb84798.zip» v:shapes="_x0000_i1358">, тогда:
<shape id="_x0000_i1359" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image589.wmz» o:><img width=«115» height=«41» src=«dopb84799.zip» v:shapes="_x0000_i1359"> умножим на 4
<shape id="_x0000_i1360" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image591.wmz» o:><img width=«100» height=«21» src=«dopb84800.zip» v:shapes="_x0000_i1360">
<shape id="_x0000_i1361" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image593.wmz» o:><img width=«123» height=«21» src=«dopb84801.zip» v:shapes="_x0000_i1361">, <shape id="_x0000_i1362" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image595.wmz» o:><img width=«93» height=«21» src=«dopb84802.zip» v:shapes="_x0000_i1362">
<shape id="_x0000_i1363" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image597.wmz» o:><img width=«165» height=«24» src=«dopb84803.zip» v:shapes="_x0000_i1363">
<shape id="_x0000_i1364" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image599.wmz» o:><img width=«71» height=«41» src=«dopb84804.zip» v:shapes="_x0000_i1364">, <shape id="_x0000_i1365" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image601.wmz» o:><img width=«29» height=«23» src=«dopb84805.zip» v:shapes="_x0000_i1365"> или <shape id="_x0000_i1366" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image603.wmz» o:><img width=«39» height=«23» src=«dopb84806.zip» v:shapes="_x0000_i1366">
1) <shape id="_x0000_i1367" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image605.wmz» o:><img width=«59» height=«21» src=«dopb84807.zip» v:shapes="_x0000_i1367">
<shape id="_x0000_i1368" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image607.wmz» o:><img width=«123» height=«24» src=«dopb84808.zip» v:shapes="_x0000_i1368">
2) <shape id="_x0000_i1369" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image609.wmz» o:><img width=«47» height=«21» src=«dopb84774.zip» v:shapes="_x0000_i1369">
<shape id="_x0000_i1370" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image610.wmz» o:><img width=«52» height=«23» src=«dopb84809.zip» v:shapes="_x0000_i1370">
Ответ: 0,0001, 10.
Пример №22
<shape id="_x0000_i1371" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image612.wmz» o:><img width=«207» height=«36» src=«dopb84810.zip» v:shapes="_x0000_i1371">
Решение
ОДЗ: <shape id="_x0000_i1372" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image581.wmz» o:><img width=«39» height=«19» src=«dopb84728.zip» v:shapes="_x0000_i1372">
<shape id="_x0000_i1373" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image614.wmz» o:><img width=«128» height=«21» src=«dopb84811.zip» v:shapes="_x0000_i1373">
<shape id="_x0000_i1374" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image616.wmz» o:><img width=«99» height=«41» src=«dopb84812.zip» v:shapes="_x0000_i1374">
Заменим: <shape id="_x0000_i1375" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image618.wmz» o:><img width=«51» height=«21» src=«dopb84813.zip» v:shapes="_x0000_i1375">, получим:
<shape id="_x0000_i1376" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image620.wmz» o:><img width=«72» height=«41» src=«dopb84814.zip» v:shapes="_x0000_i1376">, где <shape id="_x0000_i1377" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image622.wmz» o:><img width=«35» height=«19» src=«dopb84815.zip» v:shapes="_x0000_i1377">.
Решаем уравнение: <shape id="_x0000_i1378" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image624.wmz» o:><img width=«105» height=«21» src=«dopb84816.zip» v:shapes="_x0000_i1378">
<shape id="_x0000_i1379" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image626.wmz» o:><img width=«176» height=«25» src=«dopb84817.zip» v:shapes="_x0000_i1379">
<shape id="_x0000_i1380" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image628.wmz» o:><img width=«65» height=«41» src=«dopb84818.zip» v:shapes="_x0000_i1380">; <shape id="_x0000_i1381" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image630.wmz» o:><img width=«37» height=«23» src=«dopb84819.zip» v:shapes="_x0000_i1381"> или <shape id="_x0000_i1382" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image632.wmz» o:><img width=«48» height=«23» src=«dopb84820.zip» v:shapes="_x0000_i1382">
1) <shape id="_x0000_i1383" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image634.wmz» o:><img width=«51» height=«21» src=«dopb84821.zip» v:shapes="_x0000_i1383">; <shape id="_x0000_i1384" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image636.wmz» o:><img width=«59» height=«21» src=«dopb84822.zip» v:shapes="_x0000_i1384">; <shape id="_x0000_i1385" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image638.wmz» o:><img width=«49» height=«21» src=«dopb84823.zip» v:shapes="_x0000_i1385">. <shape id="_x0000_i1386" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image640.wmz» o:><img width=«40» height=«23» src=«dopb84612.zip» v:shapes="_x0000_i1386">.
2) <shape id="_x0000_i1387" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image641.wmz» o:><img width=«59» height=«21» src=«dopb84824.zip» v:shapes="_x0000_i1387">, <shape id="_x0000_i1388" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image643.wmz» o:><img width=«36» height=«19» src=«dopb84734.zip» v:shapes="_x0000_i1388">, <shape id="_x0000_i1389" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image644.wmz» o:><img width=«80» height=«21» src=«dopb84825.zip» v:shapes="_x0000_i1389">, <shape id="_x0000_i1390" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image646.wmz» o:><img width=«123» height=«44» src=«dopb84826.zip» v:shapes="_x0000_i1390">, <shape id="_x0000_i1391" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image648.wmz» o:><img width=«55» height=«24» src=«dopb84772.zip» v:shapes="_x0000_i1391">.
<imagedata src=«18604.files/image649.wmz» o:><img width=«47» height=«21» src=«dopb84774.zip» v:shapes="_x0000_i1392">; <shape id="_x0000_i1393" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image650.wmz» o:><img width=«52» height=«23» src=«dopb84809.zip» v:shapes="_x0000_i1393">; <shape id="_x0000_i1394" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image651.wmz» o:><img width=«57» height=«21» src=«dopb84745.zip» v:shapes="_x0000_i1394">; <shape id="_x0000_i1395" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image652.wmz» o:><img width=«55» height=«24» src=«dopb84827.zip» v:shapes="_x0000_i1395">.
Ответ: 0,1, 1, 10.
Пример №23
<shapetype id="_x0000_t87" coordsize=«21600,21600» o:spt=«87» adj=«1800,10800» path=«m21600,qx10800@0l10800@2qy0@11,10800@3l10800@1qy21600,21600e» filled=«f»><path arrowok=«t» o:connecttype=«custom» o:connectlocs=«21600,0;0,10800;21600,21600» textboxrect=«13963,@4,21600,@5»><img width=«9» height=«50» src=«dopb84828.zip» hspace=«12» v:shapes="_x0000_s1034"><shape id="_x0000_i1396" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image655.wmz» o:><img width=«169» height=«25» src=«dopb84829.zip» v:shapes="_x0000_i1396">
<shape id="_x0000_i1397" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image657.wmz» o:><img width=«107» height=«32» src=«dopb84830.zip» v:shapes="_x0000_i1397">
Решение
<shape id="_x0000_i1398" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image659.wmz» o:><img width=«60» height=«24» src=«dopb84831.zip» v:shapes="_x0000_i1398"> и <shape id="_x0000_i1399" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image661.wmz» o:><img width=«57» height=«21» src=«dopb84832.zip» v:shapes="_x0000_i1399">
<shape id="_x0000_i1400" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image663.wmz» o:><img width=«149» height=«24» src=«dopb84833.zip» v:shapes="_x0000_i1400"> \: <shape id="_x0000_i1401" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image665.wmz» o:><img width=«31» height=«20» src=«dopb84834.zip» v:shapes="_x0000_i1401">
<imagedata src=«18604.files/image667.wmz» o:><img width=«61» height=«21» src=«dopb84835.zip» v:shapes="_x0000_i1402">
Подставим во второе уравнение вместо <shape id="_x0000_i1403" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image669.wmz» o:><img width=«47» height=«23» src=«dopb84836.zip» v:shapes="_x0000_i1403"> число 5, получим:
<shape id="_x0000_i1404" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image671.wmz» o:><img width=«63» height=«33» src=«dopb84837.zip» v:shapes="_x0000_i1404">
<shape id="_x0000_i1405" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image673.wmz» o:><img width=«64» height=«41» src=«dopb84838.zip» v:shapes="_x0000_i1405"> или <shape id="_x0000_i1406" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image675.wmz» o:><img width=«69» height=«21» src=«dopb84839.zip» v:shapes="_x0000_i1406">
составляем систему уравнений:
<img width=«9» height=«38» src=«dopb84840.zip» hspace=«12» v:shapes="_x0000_s1035"><shape id="_x0000_i1407" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image678.wmz» o:><img width=«61» height=«21» src=«dopb84835.zip» v:shapes="_x0000_i1407">
<shape id="_x0000_i1408" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image679.wmz» o:><img width=«69» height=«21» src=«dopb84839.zip» v:shapes="_x0000_i1408"> <shape id="_x0000_i1409" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image680.wmz» o:><img width=«67» height=«21» src=«dopb84841.zip» v:shapes="_x0000_i1409">
<shape id="_x0000_i1410" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image682.wmz» o:><img width=«55» height=«19» src=«dopb84842.zip» v:shapes="_x0000_i1410"> <shape id="_x0000_i1411" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image684.wmz» o:><img width=«67» height=«21» src=«dopb84843.zip» v:shapes="_x0000_i1411">
<shape id="_x0000_i1412" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image686.wmz» o:><img width=«64» height=«19» src=«dopb84844.zip» v:shapes="_x0000_i1412"> <shape id="_x0000_i1413" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image688.wmz» o:><img width=«39» height=«21» src=«dopb84845.zip» v:shapes="_x0000_i1413">
<shape id="_x0000_i1414" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image690.wmz» o:><img width=«44» height=«19» src=«dopb84846.zip» v:shapes="_x0000_i1414">
Ответ: (13;8)
Пример №24
<shape id="_x0000_i1415" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image692.wmz» o:><img width=«289» height=«51» src=«dopb84847.zip» v:shapes="_x0000_i1415">
Решение
ОДЗ: <shape id="_x0000_i1416" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image694.wmz» o:><img width=«85» height=«128» src=«dopb84848.zip» v:shapes="_x0000_i1416"><shape id="_x0000_i1417" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image696.wmz» o:><img width=«20» height=«16» src=«dopb84849.zip» v:shapes="_x0000_i1417"><shape id="_x0000_i1418" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image698.wmz» o:><img width=«120» height=«125» src=«dopb84850.zip» v:shapes="_x0000_i1418"><shape id="_x0000_i1419" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image700.wmz» o:><img width=«20» height=«16» src=«dopb84849.zip» v:shapes="_x0000_i1419"><shape id="_x0000_i1420" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image701.wmz» o:><img width=«61» height=«51» src=«dopb84851.zip» v:shapes="_x0000_i1420">
<shape id="_x0000_i1421" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image703.wmz» o:><img width=«395» height=«39» src=«dopb84852.zip» v:shapes="_x0000_i1421">; <shape id="_x0000_i1422" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image705.wmz» o:><img width=«104» height=«25» src=«dopb84853.zip» v:shapes="_x0000_i1422">
<shape id="_x0000_i1423" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image707.wmz» o:><img width=«107» height=«21» src=«dopb84608.zip» v:shapes="_x0000_i1423">,
<shape id="_x0000_i1424" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image708.wmz» o:><img width=«165» height=«25» src=«dopb84854.zip» v:shapes="_x0000_i1424">
<shape id="_x0000_i1425" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image710.wmz» o:><img width=«63» height=«41» src=«dopb84855.zip» v:shapes="_x0000_i1425">; <shape id="_x0000_i1426" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image712.wmz» o:><img width=«39» height=«19» src=«dopb84593.zip» v:shapes="_x0000_i1426"> или <shape id="_x0000_i1427" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image713.wmz» o:><img width=«37» height=«19» src=«dopb84714.zip» v:shapes="_x0000_i1427">
<shape id="_x0000_i1428" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image714.wmz» o:><img width=«84» height=«21» src=«dopb84709.zip» v:shapes="_x0000_i1428">, <shape id="_x0000_i1429" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image715.wmz» o:><img width=«84» height=«21» src=«dopb84695.zip» v:shapes="_x0000_i1429">.
Ответ: 5.
Пример №25
<shape id="_x0000_i1430" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image716.wmz» o:><img width=«127» height=«52» src=«dopb84856.zip» v:shapes="_x0000_i1430">
Решение
ОДЗ: <shape id="_x0000_i1431" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image581.wmz» o:><img width=«39» height=«19» src=«dopb84728.zip» v:shapes="_x0000_i1431">
Прологарифмируем правую и левую части данного уравнения по основанию 10:
Получим:
<shape id="_x0000_i1432" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image718.wmz» o:><img width=«121» height=«53» src=«dopb84857.zip» v:shapes="_x0000_i1432"> или <shape id="_x0000_i1433" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image720.wmz» o:><img width=«179» height=«23» src=«dopb84858.zip» v:shapes="_x0000_i1433">
Обозначив <shape id="_x0000_i1434" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image722.wmz» o:><img width=«51» height=«21» src=«dopb84859.zip» v:shapes="_x0000_i1434">, перепишем записанное уравнение в виде:
<shape id="_x0000_i1435" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image724.wmz» o:><img width=«189» height=«24» src=«dopb84860.zip» v:shapes="_x0000_i1435">.
Решая его относительно <shape id="_x0000_i1436" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image726.wmz» o:><img width=«15» height=«17» src=«dopb84861.zip» v:shapes="_x0000_i1436">, находим <shape id="_x0000_i1437" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image728.wmz» o:><img width=«44» height=«23» src=«dopb84862.zip» v:shapes="_x0000_i1437">, <shape id="_x0000_i1438" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image730.wmz» o:><img width=«79» height=«23» src=«dopb84863.zip» v:shapes="_x0000_i1438">.
Используя обозначения <shape id="_x0000_i1439" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image732.wmz» o:><img width=«51» height=«21» src=«dopb84859.zip» v:shapes="_x0000_i1439">, из первого решения квадратного уравнения имеем <shape id="_x0000_i1440" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image733.wmz» o:><img width=«49» height=«21» src=«dopb84792.zip» v:shapes="_x0000_i1440">. Отсюда <shape id="_x0000_i1441" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image734.wmz» o:><img width=«57» height=«23» src=«dopb84864.zip» v:shapes="_x0000_i1441">. Используя решение <shape id="_x0000_i1442" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image736.wmz» o:><img width=«20» height=«23» src=«dopb84865.zip» v:shapes="_x0000_i1442">, получаем <shape id="_x0000_i1443" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image738.wmz» o:><img width=«81» height=«21» src=«dopb84866.zip» v:shapes="_x0000_i1443">. Преобразуем правую часть этого уравнения:
<shape id="_x0000_i1444" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image740.wmz» o:><img width=«91» height=«21» src=«dopb84867.zip» v:shapes="_x0000_i1444">. Значит, <shape id="_x0000_i1445" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image742.wmz» o:><img width=«69» height=«21» src=«dopb84868.zip» v:shapes="_x0000_i1445">, т.е. <shape id="_x0000_i1446" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image744.wmz» o:><img width=«51» height=«23» src=«dopb84869.zip» v:shapes="_x0000_i1446">.
Ответ: 30, 100.
Пример №26
<shape id="_x0000_i1447" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image746.wmz» o:><img width=«160» height=«45» src=«dopb84870.zip» v:shapes="_x0000_i1447">
Решение
Так как <shape id="_x0000_i1448" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image748.wmz» o:><img width=«63» height=«21» src=«dopb84871.zip» v:shapes="_x0000_i1448">, то при <shape id="_x0000_i1449" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image750.wmz» o:><img width=«39» height=«19» src=«dopb84728.zip» v:shapes="_x0000_i1449"> и <shape id="_x0000_i1450" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image751.wmz» o:><img width=«39» height=«19» src=«dopb84706.zip» v:shapes="_x0000_i1450"> имеем равносильное уравнение:
<shape id="_x0000_i1451" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image752.wmz» o:><img width=«79» height=«25» src=«dopb84872.zip» v:shapes="_x0000_i1451"> или <shape id="_x0000_i1452" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image754.wmz» o:><img width=«60» height=«19» src=«dopb84694.zip» v:shapes="_x0000_i1452">
<shape id="_x0000_i1453" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image755.wmz» o:><img width=«84» height=«21» src=«dopb84695.zip» v:shapes="_x0000_i1453">.
<shape id="_x0000_i1454" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image756.wmz» o:><img width=«69» height=«19» src=«dopb84873.zip» v:shapes="_x0000_i1454">, <shape id="_x0000_i1455" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image758.wmz» o:><img width=«92» height=«21» src=«dopb84874.zip» v:shapes="_x0000_i1455">
Ответ: 5.
Пример № 27
<shape id="_x0000_i1456" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image760.wmz» o:><img width=«134» height=«37» src=«dopb84875.zip» v:shapes="_x0000_i1456">
Решение
ОДЗ: <shape id="_x0000_i1457" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image581.wmz» o:><img width=«39» height=«19» src=«dopb84728.zip» v:shapes="_x0000_i1457">
Так как обе части уравнения положительны, то прологарифмируем по основанию 10:
<shape id="_x0000_i1458" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image762.wmz» o:><img width=«143» height=«21» src=«dopb84876.zip» v:shapes="_x0000_i1458">
<shape id="_x0000_i1459" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image764.wmz» o:><img width=«115» height=«24» src=«dopb84877.zip» v:shapes="_x0000_i1459">
<shape id="_x0000_i1460" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image766.wmz» o:><img width=«51» height=«21» src=«dopb84736.zip» v:shapes="_x0000_i1460">, <shape id="_x0000_i1461" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image767.wmz» o:><img width=«95» height=«24» src=«dopb84878.zip» v:shapes="_x0000_i1461">
<shape id="_x0000_i1462" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image769.wmz» o:><img width=«177» height=«25» src=«dopb84879.zip» v:shapes="_x0000_i1462">
<shape id="_x0000_i1463" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image771.wmz» o:><img width=«61» height=«41» src=«dopb84880.zip» v:shapes="_x0000_i1463">; <shape id="_x0000_i1464" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image773.wmz» o:><img width=«52» height=«23» src=«dopb84881.zip» v:shapes="_x0000_i1464"> или <shape id="_x0000_i1465" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image775.wmz» o:><img width=«47» height=«23» src=«dopb84882.zip» v:shapes="_x0000_i1465">
1) <shape id="_x0000_i1466" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image777.wmz» o:><img width=«57» height=«21» src=«dopb84745.zip» v:shapes="_x0000_i1466"> 2) <shape id="_x0000_i1467" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image778.wmz» o:><img width=«49» height=«21» src=«dopb84792.zip» v:shapes="_x0000_i1467">
<shape id="_x0000_i1468" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image779.wmz» o:><img width=«97» height=«24» src=«dopb84883.zip» v:shapes="_x0000_i1468"> <shape id="_x0000_i1469" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image781.wmz» o:><img width=«99» height=«24» src=«dopb84794.zip» v:shapes="_x0000_i1469">
Ответ: 0.1, 100.
Пример №28
<shape id="_x0000_i1470" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image782.wmz» o:><img width=«133» height=«42» src=«dopb84884.zip» v:shapes="_x0000_i1470">
Решение
ОДЗ: <shape id="_x0000_i1471" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image581.wmz» o:><img width=«39» height=«19» src=«dopb84728.zip» v:shapes="_x0000_i1471">
Так как обе части уравнения положительны, то прологарифмируем по основанию 3:
<shape id="_x0000_i1472" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image784.wmz» o:><img width=«117» height=«24» src=«dopb84885.zip» v:shapes="_x0000_i1472">
<shape id="_x0000_i1473" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image786.wmz» o:><img width=«197» height=«24» src=«dopb84886.zip» v:shapes="_x0000_i1473">
<shape id="_x0000_i1474" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image788.wmz» o:><img width=«65» height=«24» src=«dopb84887.zip» v:shapes="_x0000_i1474"> и <shape id="_x0000_i1475" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image790.wmz» o:><img width=«61» height=«24» src=«dopb84888.zip» v:shapes="_x0000_i1475">, поэтому
<shape id="_x0000_i1476" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image792.wmz» o:><img width=«128» height=«24» src=«dopb84889.zip» v:shapes="_x0000_i1476">
<shape id="_x0000_i1477" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image794.wmz» o:><img width=«143» height=«27» src=«dopb84890.zip» v:shapes="_x0000_i1477">
<shape id="_x0000_i1478" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image796.wmz» o:><img width=«139» height=«25» src=«dopb84891.zip» v:shapes="_x0000_i1478">
Пусть <shape id="_x0000_i1479" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image798.wmz» o:><img width=«61» height=«24» src=«dopb84892.zip» v:shapes="_x0000_i1479">, тогда <shape id="_x0000_i1480" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image800.wmz» o:><img width=«87» height=«21» src=«dopb84893.zip» v:shapes="_x0000_i1480">
<shape id="_x0000_i1481" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image802.wmz» o:><img width=«49» height=«23» src=«dopb84894.zip» v:shapes="_x0000_i1481"> или <shape id="_x0000_i1482" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image804.wmz» o:><img width=«39» height=«23» src=«dopb84806.zip» v:shapes="_x0000_i1482">.
1) <shape id="_x0000_i1483" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image805.wmz» o:><img width=«73» height=«24» src=«dopb84895.zip» v:shapes="_x0000_i1483">
<shape id="_x0000_i1484" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image807.wmz» o:><img width=«119» height=«41» src=«dopb84896.zip» v:shapes="_x0000_i1484">;
2) <shape id="_x0000_i1485" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image809.wmz» o:><img width=«61» height=«24» src=«dopb84897.zip» v:shapes="_x0000_i1485">
<shape id="_x0000_i1486" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image811.wmz» o:><img width=«44» height=«23» src=«dopb84898.zip» v:shapes="_x0000_i1486">
Ответ: <shape id="_x0000_i1487" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image813.wmz» o:><img width=«15» height=«41» src=«dopb84899.zip» v:shapes="_x0000_i1487">, 3.
Пример №29
<shape id="_x0000_i1488" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image815.wmz» o:><img width=«241» height=«38» src=«dopb84900.zip» v:shapes="_x0000_i1488">
Решение
1) <shape id="_x0000_i1489" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image817.wmz» o:><img width=«36» height=«15» src=«dopb84901.zip» v:shapes="_x0000_i1489"><shape id="_x0000_i1490" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image819.wmz» o:><img width=«25» height=«19» src=«dopb84902.zip» v:shapes="_x0000_i1490">, т.к. 0 в любой степени не равен 1.
2) <shape id="_x0000_i1491" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image821.wmz» o:><img width=«41» height=«27» src=«dopb84903.zip» v:shapes="_x0000_i1491">= 1, <shape id="_x0000_i1492" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image817.wmz» o:><img width=«36» height=«15» src=«dopb84901.zip» v:shapes="_x0000_i1492">=1, <shape id="_x0000_i1493" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image823.wmz» o:><img width=«60» height=«23» src=«dopb84904.zip» v:shapes="_x0000_i1493">, <shape id="_x0000_i1494" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image825.wmz» o:><img width=«37» height=«19» src=«dopb84905.zip» v:shapes="_x0000_i1494"> или
<shape id="_x0000_i1495" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image817.wmz» o:><img width=«36» height=«15» src=«dopb84901.zip» v:shapes="_x0000_i1495">=-1, <shape id="_x0000_i1496" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image827.wmz» o:><img width=«85» height=«23» src=«dopb84906.zip» v:shapes="_x0000_i1496">, <shape id="_x0000_i1497" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image829.wmz» o:><img width=«37» height=«19» src=«dopb84905.zip» v:shapes="_x0000_i1497">.
Так как 1 в любой степени равна 1, то это решения.
3) <imagedata src=«18604.files/image830.wmz» o:><img width=«215» height=«40» src=«dopb84907.zip» v:shapes="_x0000_i1498"> (т.к. <shape id="_x0000_i1499" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image832.wmz» o:><img width=«61» height=«19» src=«dopb84908.zip» v:shapes="_x0000_i1499">)
При <shape id="_x0000_i1500" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image834.wmz» o:><img width=«63» height=«27» src=«dopb84909.zip» v:shapes="_x0000_i1500"> все решения принадлежат уравнению <shape id="_x0000_i1501" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image836.wmz» o:><img width=«167» height=«21» src=«dopb84910.zip» v:shapes="_x0000_i1501">. <shape id="_x0000_i1502" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image838.wmz» o:><img width=«45» height=«19» src=«dopb84911.zip» v:shapes="_x0000_i1502"> или <shape id="_x0000_i1503" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image840.wmz» o:><img width=«61» height=«41» src=«dopb84912.zip» v:shapes="_x0000_i1503">.
При <shape id="_x0000_i1504" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image838.wmz» o:><img width=«45» height=«19» src=«dopb84911.zip» v:shapes="_x0000_i1504"> <imagedata src=«18604.files/image842.wmz» o:><img width=«12» height=«23» src=«dopb84913.zip» v:shapes="_x0000_i1505"><shape id="_x0000_i1506" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image817.wmz» o:><img width=«36» height=«15» src=«dopb84901.zip» v:shapes="_x0000_i1506">= 0, что не удовлетворяет уравнению <shape id="_x0000_i1507" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image844.wmz» o:><img width=«32» height=«23» src=«dopb84914.zip» v:shapes="_x0000_i1507">
<shape id="_x0000_i1508" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image842.wmz» o:><img width=«12» height=«23» src=«dopb84913.zip» v:shapes="_x0000_i1508"><shape id="_x0000_i1509" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image840.wmz» o:><img width=«61» height=«41» src=«dopb84912.zip» v:shapes="_x0000_i1509">, <shape id="_x0000_i1510" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image846.wmz» o:><img width=«169» height=«41» src=«dopb84915.zip» v:shapes="_x0000_i1510">
Ответ: <shape id="_x0000_i1511" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image848.wmz» o:><img width=«127» height=«41» src=«dopb84916.zip» v:shapes="_x0000_i1511">, <shape id="_x0000_i1512" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image850.wmz» o:><img width=«37» height=«19» src=«dopb84905.zip» v:shapes="_x0000_i1512">.
<shape id="_x0000_i1513" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image851.wmz» o:><img width=«61» height=«23» src=«dopb84917.zip» v:shapes="_x0000_i1513">, <shape id="_x0000_i1514" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image853.wmz» o:><img width=«37» height=«19» src=«dopb84905.zip» v:shapes="_x0000_i1514">.
<shape id="_x0000_i1515" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image854.wmz» o:><img width=«87» height=«24» src=«dopb84918.zip» v:shapes="_x0000_i1515">, <shape id="_x0000_i1516" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image853.wmz» o:><img width=«37» height=«19» src=«dopb84905.zip» v:shapes="_x0000_i1516">.
Пример №30
<shape id="_x0000_i1517" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image856.wmz» o:><img width=«212» height=«67» src=«dopb84919.zip» v:shapes="_x0000_i1517">
Решение
ОДЗ: <shape id="_x0000_i1518" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image858.wmz» o:><img width=«149» height=«65» src=«dopb84920.zip» v:shapes="_x0000_i1518"><shape id="_x0000_i1519" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image860.wmz» o:><img width=«20» height=«16» src=«dopb84849.zip» v:shapes="_x0000_i1519"><shape id="_x0000_i1520" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image861.wmz» o:><img width=«126» height=«65» src=«dopb84921.zip» v:shapes="_x0000_i1520">
<shape id="_x0000_i1521" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image863.wmz» o:><img width=«85» height=«36» src=«dopb84922.zip» v:shapes="_x0000_i1521">= <shape id="_x0000_i1522" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image865.wmz» o:><img width=«60» height=«33» src=«dopb84923.zip» v:shapes="_x0000_i1522">
1) <shape id="_x0000_i1523" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image867.wmz» o:><img width=«67» height=«21» src=«dopb84924.zip» v:shapes="_x0000_i1523">, <shape id="_x0000_i1524" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image869.wmz» o:><img width=«103» height=«27» src=«dopb84925.zip» v:shapes="_x0000_i1524">, <shape id="_x0000_i1525" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image871.wmz» o:><img width=«112» height=«25» src=«dopb84926.zip» v:shapes="_x0000_i1525">.
2) Так как <shape id="_x0000_i1526" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image873.wmz» o:><img width=«69» height=«21» src=«dopb84927.zip» v:shapes="_x0000_i1526">, то остальные решения получаем из уравнения <shape id="_x0000_i1527" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image875.wmz» o:><img width=«87» height=«44» src=«dopb84928.zip» v:shapes="_x0000_i1527">: Отсюда <shape id="_x0000_i1528" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image877.wmz» o:><img width=«59» height=«19» src=«dopb84929.zip» v:shapes="_x0000_i1528"> или <shape id="_x0000_i1529" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image879.wmz» o:><img width=«75» height=«41» src=«dopb84930.zip» v:shapes="_x0000_i1529">. <shape id="_x0000_i1530" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image881.wmz» o:><img width=«59» height=«19» src=«dopb84929.zip» v:shapes="_x0000_i1530"> <shape id="_x0000_i1531" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image882.wmz» o:><img width=«61» height=«24» src=«dopb84931.zip» v:shapes="_x0000_i1531">, <shape id="_x0000_i1532" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image853.wmz» o:><img width=«37» height=«19» src=«dopb84905.zip» v:shapes="_x0000_i1532"> и <shape id="_x0000_i1533" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image879.wmz» o:><img width=«75» height=«41» src=«dopb84930.zip» v:shapes="_x0000_i1533"> <shape id="_x0000_i1534" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image842.wmz» o:><img width=«12» height=«23» src=«dopb84913.zip» v:shapes="_x0000_i1534"><shape id="_x0000_i1535" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image884.wmz» o:><img width=«109» height=«41» src=«dopb84932.zip» v:shapes="_x0000_i1535">, <shape id="_x0000_i1536" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image853.wmz» o:><img width=«37» height=«19» src=«dopb84905.zip» v:shapes="_x0000_i1536">.
Ответ: <shape id="_x0000_i1537" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image886.wmz» o:><img width=«24» height=«24» src=«dopb84933.zip» v:shapes="_x0000_i1537">, -<shape id="_x0000_i1538" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image886.wmz» o:><img width=«24» height=«24» src=«dopb84933.zip» v:shapes="_x0000_i1538">, <shape id="_x0000_i1539" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image888.wmz» o:><img width=«29» height=«19» src=«dopb84934.zip» v:shapes="_x0000_i1539"> и <shape id="_x0000_i1540" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image890.wmz» o:><img width=«77» height=«41» src=«dopb84935.zip» v:shapes="_x0000_i1540">, <shape id="_x0000_i1541" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image853.wmz» o:><img width=«37» height=«19» src=«dopb84905.zip» v:shapes="_x0000_i1541">.
Пример №31
<shape id="_x0000_i1542" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image892.wmz» o:><img width=«221» height=«51» src=«dopb84936.zip» v:shapes="_x0000_i1542">
Решение
<shape id="_x0000_i1543" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image894.wmz» o:><img width=«160» height=«44» src=«dopb84937.zip» v:shapes="_x0000_i1543">
1) <shape id="_x0000_i1544" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image896.wmz» o:><img width=«65» height=«27» src=«dopb84938.zip» v:shapes="_x0000_i1544"> или <shape id="_x0000_i1545" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image898.wmz» o:><img width=«39» height=«19» src=«dopb84708.zip» v:shapes="_x0000_i1545">, <shape id="_x0000_i1546" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image899.wmz» o:><img width=«64» height=«41» src=«dopb84939.zip» v:shapes="_x0000_i1546"> и <shape id="_x0000_i1547" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image901.wmz» o:><img width=«64» height=«41» src=«dopb84940.zip» v:shapes="_x0000_i1547">. Это решение. <shape id="_x0000_i1548" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image903.wmz» o:><img width=«44» height=«23» src=«dopb84591.zip» v:shapes="_x0000_i1548">.
2) <shape id="_x0000_i1549" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image904.wmz» o:><img width=«63» height=«27» src=«dopb84941.zip» v:shapes="_x0000_i1549">, <shape id="_x0000_i1550" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image906.wmz» o:><img width=«44» height=«23» src=«dopb84716.zip» v:shapes="_x0000_i1550"> и <shape id="_x0000_i1551" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image907.wmz» o:><img width=«44» height=«24» src=«dopb84942.zip» v:shapes="_x0000_i1551">
3) Так как <shape id="_x0000_i1552" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image909.wmz» o:><img width=«65» height=«27» src=«dopb84943.zip» v:shapes="_x0000_i1552">, то <shape id="_x0000_i1553" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image911.wmz» o:><img width=«89» height=«41» src=«dopb84944.zip» v:shapes="_x0000_i1553">;
<shape id="_x0000_i1554" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image913.wmz» o:><img width=«119» height=«23» src=«dopb84945.zip» v:shapes="_x0000_i1554">;
<shape id="_x0000_i1555" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image915.wmz» o:><img width=«107» height=«19» src=«dopb84946.zip» v:shapes="_x0000_i1555">
<shape id="_x0000_i1556" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image917.wmz» o:><img width=«107» height=«19» src=«dopb84947.zip» v:shapes="_x0000_i1556">
<shape id="_x0000_i1557" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image919.wmz» o:><img width=«52» height=«19» src=«dopb84948.zip» v:shapes="_x0000_i1557">
<shape id="_x0000_i1558" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image921.wmz» o:><img width=«84» height=«41» src=«dopb84949.zip» v:shapes="_x0000_i1558">; <shape id="_x0000_i1559" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image923.wmz» o:><img width=«77» height=«45» src=«dopb84950.zip» v:shapes="_x0000_i1559">. Это решение.
Ответ: <shape id="_x0000_i1560" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image925.wmz» o:><img width=«24» height=«41» src=«dopb84951.zip» v:shapes="_x0000_i1560">; 5; 3; 4.
Пример №32
<shape id="_x0000_i1561" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image927.wmz» o:><img width=«323» height=«53» src=«dopb84952.zip» v:shapes="_x0000_i1561">
Решение
<shape id="_x0000_i1562" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image929.wmz» o:><img width=«71» height=«21» src=«dopb84953.zip» v:shapes="_x0000_i1562"> при всех <shape id="_x0000_i1563" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image108.wmz» o:><img width=«13» height=«15» src=«dopb84711.zip» v:shapes="_x0000_i1563">
<shape id="_x0000_i1564" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image931.wmz» o:><img width=«254» height=«43» src=«dopb84954.zip» v:shapes="_x0000_i1564">
<shape id="_x0000_i1565" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image933.wmz» o:><img width=«192» height=«33» src=«dopb84955.zip» v:shapes="_x0000_i1565">
1) <shape id="_x0000_i1566" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image935.wmz» o:><img width=«75» height=«24» src=«dopb84956.zip» v:shapes="_x0000_i1566">, <shape id="_x0000_i1567" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image937.wmz» o:><img width=«53» height=«21» src=«dopb84957.zip» v:shapes="_x0000_i1567"> - решений нет.
2)<shape id="_x0000_i1568" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image939.wmz» o:><img width=«89» height=«24» src=«dopb84958.zip» v:shapes="_x0000_i1568">. Потому при <shape id="_x0000_i1569" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image941.wmz» o:><img width=«64» height=«21» src=«dopb84959.zip» v:shapes="_x0000_i1569"> левая часть равна единице, а правая нет. Это решение.
3) <shape id="_x0000_i1570" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image943.wmz» o:><img width=«180» height=«33» src=«dopb84960.zip» v:shapes="_x0000_i1570">;
<shape id="_x0000_i1571" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image945.wmz» o:><img width=«268» height=«45» src=«dopb84961.zip» v:shapes="_x0000_i1571">;
<imagedata src=«18604.files/image947.wmz» o:><img width=«89» height=«24» src=«dopb84962.zip» v:shapes="_x0000_i1572">;
<shape id="_x0000_i1573" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image949.wmz» o:><img width=«124» height=«45» src=«dopb84963.zip» v:shapes="_x0000_i1573"> ;
<shape id="_x0000_i1574" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image951.wmz» o:><img width=«141» height=«41» src=«dopb84964.zip» v:shapes="_x0000_i1574">;
<shape id="_x0000_i1575" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image953.wmz» o:><img width=«117» height=«41» src=«dopb84965.zip» v:shapes="_x0000_i1575">;
<shape id="_x0000_i1576" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image955.wmz» o:><img width=«101» height=«24» src=«dopb84966.zip» v:shapes="_x0000_i1576">;
<shape id="_x0000_i1577" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image957.wmz» o:><img width=«41» height=«23» src=«dopb84967.zip» v:shapes="_x0000_i1577"> и <shape id="_x0000_i1578" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image959.wmz» o:><img width=«55» height=«23» src=«dopb84968.zip» v:shapes="_x0000_i1578">;
<shape id="_x0000_i1579" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image961.wmz» o:><img width=«84» height=«24» src=«dopb84969.zip» v:shapes="_x0000_i1579">; <shape id="_x0000_i1580" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image963.wmz» o:><img width=«73» height=«21» src=«dopb84970.zip» v:shapes="_x0000_i1580">;
<shape id="_x0000_i1581" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image965.wmz» o:><img width=«43» height=«23» src=«dopb84603.zip» v:shapes="_x0000_i1581">; <shape id="_x0000_i1582" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image966.wmz» o:><img width=«53» height=«23» src=«dopb84971.zip» v:shapes="_x0000_i1582">;
<shape id="_x0000_i1583" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image968.wmz» o:><img width=«96» height=«24» src=«dopb84972.zip» v:shapes="_x0000_i1583">;
<shape id="_x0000_i1584" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image970.wmz» o:><img width=«84» height=«21» src=«dopb84973.zip» v:shapes="_x0000_i1584">;
<shape id="_x0000_i1585" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image972.wmz» o:><img width=«111» height=«21» src=«dopb84974.zip» v:shapes="_x0000_i1585"> - решений нет.
Ответ: -3, 3.
Пример №33
Решить графически уравнение:
<shape id="_x0000_i1586" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image974.wmz» o:><img width=«154» height=«64» src=«dopb84975.zip» v:shapes="_x0000_i1586">
Решение
У функции <shape id="_x0000_i1587" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image976.wmz» o:><img width=«115» height=«53» src=«dopb84976.zip» v:shapes="_x0000_i1587"> Д(y): x > 0 и log2 x > 0, т.е.,
x > 1. обл. определения х > 1.
А теперь: <shape id="_x0000_i1588" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image842.wmz» o:><img width=«12» height=«23» src=«dopb84913.zip» v:shapes="_x0000_i1588"><shape id="_x0000_i1589" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image978.wmz» o:><img width=«130» height=«51» src=«dopb84977.zip» v:shapes="_x0000_i1589"> (формула перехода к новому основанию и определение логарифма).
Тогда <shape id="_x0000_i1590" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image980.wmz» o:><img width=«140» height=«24» src=«dopb84978.zip» v:shapes="_x0000_i1590"> (определение логарифма: <shape id="_x0000_i1591" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image982.wmz» o:><img width=«92» height=«30» src=«dopb84979.zip» v:shapes="_x0000_i1591">).
Так, что нужно только учитывать, что Д(у): x > 0.
Построим график функции (рис III.1).
<img width=«12» height=«315» src=«dopb84980.zip» v:shapes="_x0000_s1036">
у
<img width=«405» height=«185» src=«dopb84981.zip» v:shapes="_x0000_s1037"> <shape id="_x0000_i1592" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image986.wmz» o:><img width=«71» height=«23» src=«dopb84982.zip» v:shapes="_x0000_i1592">
<shape id="_x0000_i1593" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image988.wmz» o:><img width=«39» height=«21» src=«dopb84983.zip» v:shapes="_x0000_i1593">
<img width=«2» height=«74» src=«dopb84984.zip» hspace=«12» v:shapes="_x0000_s1038"><img width=«525» height=«4» src=«dopb84985.zip» hspace=«12» v:shapes="_x0000_s1039"> 2
1
<img width=«549» height=«12» src=«dopb84986.zip» v:shapes="_x0000_s1040">
0 1 4 х
Рис. III.1.
Ответ: (4; 2).
Пример №34
Решить систему уравнений:
<shape id="_x0000_i1594" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image993.wmz» o:><img width=«20» height=«75» src=«dopb84987.zip» v:shapes="_x0000_i1594"> <shape id="_x0000_i1595" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image995.wmz» o:><img width=«167» height=«92» src=«dopb84988.zip» v:shapes="_x0000_i1595">
Решение:
<shape id="_x0000_i1596" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image997.wmz» o:><img width=«84» height=«25» src=«dopb84989.zip» v:shapes="_x0000_i1596">
По определению логарифма имеем:
<shape id="_x0000_i1597" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image999.wmz» o:><img width=«77» height=«69» src=«dopb84990.zip» v:shapes="_x0000_i1597"><shape id="_x0000_i1598" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1001.wmz» o:><img width=«20» height=«16» src=«dopb84849.zip» v:shapes="_x0000_i1598"> <shape id="_x0000_i1599" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1002.wmz» o:><img width=«55» height=«69» src=«dopb84991.zip» v:shapes="_x0000_i1599"> <shape id="_x0000_i1600" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1004.wmz» o:><img width=«20» height=«16» src=«dopb84849.zip» v:shapes="_x0000_i1600"> <shape id="_x0000_i1601" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1005.wmz» o:><img width=«53» height=«69» src=«dopb84992.zip» v:shapes="_x0000_i1601"> <shape id="_x0000_i1602" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1007.wmz» o:><img width=«20» height=«16» src=«dopb84849.zip» v:shapes="_x0000_i1602"> <shape id="_x0000_i1603" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1008.wmz» o:><img width=«63» height=«51» src=«dopb84993.zip» v:shapes="_x0000_i1603"><shape id="_x0000_i1604" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1010.wmz» o:><img width=«20» height=«16» src=«dopb84849.zip» v:shapes="_x0000_i1604"> <shape id="_x0000_i1605" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1011.wmz» o:><img width=«57» height=«69» src=«dopb84994.zip» v:shapes="_x0000_i1605"> <shape id="_x0000_i1606" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1013.wmz» o:><img width=«20» height=«16» src=«dopb84849.zip» v:shapes="_x0000_i1606"> <shape id="_x0000_i1607" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1014.wmz» o:><img width=«75» height=«44» src=«dopb84995.zip» v:shapes="_x0000_i1607">.
Прологарифмируем первое уравнение системы по основанию х.
<shape id="_x0000_i1608" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1016.wmz» o:><img width=«215» height=«91» src=«dopb84996.zip» v:shapes="_x0000_i1608"> <shape id="_x0000_i1609" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1018.wmz» o:><img width=«20» height=«16» src=«dopb84849.zip» v:shapes="_x0000_i1609"> <shape id="_x0000_i1610" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1019.wmz» o:><img width=«201» height=«77» src=«dopb84997.zip» v:shapes="_x0000_i1610"> <shape id="_x0000_i1611" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1021.wmz» o:><img width=«20» height=«16» src=«dopb84849.zip» v:shapes="_x0000_i1611"> <shape id="_x0000_i1612" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1022.wmz» o:><img width=«151» height=«53» src=«dopb84998.zip» v:shapes="_x0000_i1612"> .
Из второго уравнения системы выразим у через х:
<shape id="_x0000_i1613" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1024.wmz» o:><img width=«77» height=«24» src=«dopb84999.zip» v:shapes="_x0000_i1613">, <shape id="_x0000_i1614" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1026.wmz» o:><img width=«73» height=«44» src=«dopb85000.zip» v:shapes="_x0000_i1614">
Тогда: <shape id="_x0000_i1615" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1028.wmz» o:><img width=«223» height=«44» src=«dopb85001.zip» v:shapes="_x0000_i1615">
Пусть <shape id="_x0000_i1616" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1030.wmz» o:><img width=«100» height=«44» src=«dopb85002.zip» v:shapes="_x0000_i1616">, <shape id="_x0000_i1617" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1032.wmz» o:><img width=«93» height=«21» src=«dopb85003.zip» v:shapes="_x0000_i1617">, Д = (-5)2 -4*1*4 = 9, <shape id="_x0000_i1618" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1034.wmz» o:><img width=«59» height=«41» src=«dopb85004.zip» v:shapes="_x0000_i1618">, <shape id="_x0000_i1619" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1036.wmz» o:><img width=«37» height=«23» src=«dopb84819.zip» v:shapes="_x0000_i1619"> или <shape id="_x0000_i1620" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1037.wmz» o:><img width=«41» height=«23» src=«dopb85005.zip» v:shapes="_x0000_i1620">.
1) <shape id="_x0000_i1621" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1039.wmz» o:><img width=«100» height=«44» src=«dopb85006.zip» v:shapes="_x0000_i1621"> 2) <shape id="_x0000_i1622" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1041.wmz» o:><img width=«103» height=«44» src=«dopb85007.zip» v:shapes="_x0000_i1622">
<shape id="_x0000_i1623" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1043.wmz» o:><img width=«72» height=«44» src=«dopb85008.zip» v:shapes="_x0000_i1623"> <shape id="_x0000_i1624" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1045.wmz» o:><img width=«79» height=«44» src=«dopb85009.zip» v:shapes="_x0000_i1624">
<shape id="_x0000_i1625" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1047.wmz» o:><img width=«100» height=«21» src=«dopb85010.zip» v:shapes="_x0000_i1625"> <shape id="_x0000_i1626" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1049.wmz» o:><img width=«108» height=«21» src=«dopb85011.zip» v:shapes="_x0000_i1626">
Д = (-3)2 – 4*1*(-4) = 25 пусть <shape id="_x0000_i1627" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1051.wmz» o:><img width=«47» height=«21» src=«dopb85012.zip» v:shapes="_x0000_i1627">, тогда
<shape id="_x0000_i1628" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1053.wmz» o:><img width=«63» height=«41» src=«dopb85013.zip» v:shapes="_x0000_i1628"> <shape id="_x0000_i1629" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1055.wmz» o:><img width=«100» height=«21» src=«dopb85014.zip» v:shapes="_x0000_i1629">
<shape id="_x0000_i1630" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1057.wmz» o:><img width=«51» height=«23» src=«dopb84582.zip» v:shapes="_x0000_i1630"> или <shape id="_x0000_i1631" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1058.wmz» o:><img width=«45» height=«23» src=«dopb84699.zip» v:shapes="_x0000_i1631"> Д = (-1)2 – 4*3*4 = -47<0
<shape id="_x0000_i1632" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1059.wmz» o:><img width=«52» height=«23» src=«dopb84881.zip» v:shapes="_x0000_i1632"> или <shape id="_x0000_i1633" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1060.wmz» o:><img width=«47» height=«23» src=«dopb85015.zip» v:shapes="_x0000_i1633"> корней нет
(-1,-1) – удовлетворяет ОДЗ
(4,4) решение системы уравнений.
Ответ: (4, 4).
Пример №35
Решите систему уравнений:
<shape id="_x0000_i1634" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1062.wmz» o:><img width=«225» height=«72» src=«dopb85016.zip» v:shapes="_x0000_i1634">
Решение.
<shape id="_x0000_i1635" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image997.wmz» o:><img width=«84» height=«25» src=«dopb84989.zip» v:shapes="_x0000_i1635">
По определению логарифма имеем:
<shape id="_x0000_i1636" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1064.wmz» o:><img width=«84» height=«112» src=«dopb85017.zip» v:shapes="_x0000_i1636"> <shape id="_x0000_i1637" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1066.wmz» o:><img width=«20» height=«16» src=«dopb84849.zip» v:shapes="_x0000_i1637"> <shape id="_x0000_i1638" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1067.wmz» o:><img width=«75» height=«112» src=«dopb85018.zip» v:shapes="_x0000_i1638"> <shape id="_x0000_i1639" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1069.wmz» o:><img width=«20» height=«16» src=«dopb84849.zip» v:shapes="_x0000_i1639"> <shape id="_x0000_i1640" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1070.wmz» o:><img width=«93» height=«136» src=«dopb85019.zip» v:shapes="_x0000_i1640">
Основание логарифма может быть:
1) <shape id="_x0000_i1641" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1072.wmz» o:><img width=«80» height=«19» src=«dopb85020.zip» v:shapes="_x0000_i1641"> (дробное)
<shape id="_x0000_i1642" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1074.wmz» o:><img width=«72» height=«19» src=«dopb85021.zip» v:shapes="_x0000_i1642">
(-1, 0) – не удовлетворяет ОДЗ.
2) <shape id="_x0000_i1643" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1076.wmz» o:><img width=«56» height=«19» src=«dopb85022.zip» v:shapes="_x0000_i1643">
<shape id="_x0000_i1644" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1078.wmz» o:><img width=«37» height=«19» src=«dopb85023.zip» v:shapes="_x0000_i1644">
Выполним преобразования:
<shape id="_x0000_i1645" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1080.wmz» o:><img width=«311» height=«88» src=«dopb85024.zip» v:shapes="_x0000_i1645">
Прологарифмируем первое уравнение системы по основанию х:
<shape id="_x0000_i1646" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1082.wmz» o:><img width=«199» height=«51» src=«dopb85025.zip» v:shapes="_x0000_i1646">,
<shape id="_x0000_i1647" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1084.wmz» o:><img width=«65» height=«24» src=«dopb85026.zip» v:shapes="_x0000_i1647">, <shape id="_x0000_i1648" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1086.wmz» o:><img width=«143» height=«45» src=«dopb85027.zip» v:shapes="_x0000_i1648">,
<shape id="_x0000_i1649" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1088.wmz» o:><img width=«160» height=«52» src=«dopb85028.zip» v:shapes="_x0000_i1649">
<shape id="_x0000_i1650" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1090.wmz» o:><img width=«125» height=«25» src=«dopb85029.zip» v:shapes="_x0000_i1650"> или <shape id="_x0000_i1651" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1092.wmz» o:><img width=«148» height=«25» src=«dopb85030.zip» v:shapes="_x0000_i1651">
Пусть <shape id="_x0000_i1652" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1094.wmz» o:><img width=«60» height=«24» src=«dopb85031.zip» v:shapes="_x0000_i1652">, тогда <shape id="_x0000_i1653" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1096.wmz» o:><img width=«85» height=«21» src=«dopb85032.zip» v:shapes="_x0000_i1653">
Д = (-)2 -4*1*(-2) = 9
<shape id="_x0000_i1654" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1098.wmz» o:><img width=«48» height=«23» src=«dopb85033.zip» v:shapes="_x0000_i1654"> или <shape id="_x0000_i1655" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1100.wmz» o:><img width=«41» height=«23» src=«dopb85034.zip» v:shapes="_x0000_i1655">
<shape id="_x0000_i1656" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1102.wmz» o:><img width=«157» height=«41» src=«dopb85035.zip» v:shapes="_x0000_i1656">
<img width=«2» height=«38» src=«dopb85036.zip» v:shapes="_x0000_s1041"><shape id="_x0000_i1657" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1105.wmz» o:><img width=«171» height=«45» src=«dopb85037.zip» v:shapes="_x0000_i1657">: (х+1)
<shape id="_x0000_i1658" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1107.wmz» o:><img width=«81» height=«41» src=«dopb85038.zip» v:shapes="_x0000_i1658">
<shape id="_x0000_i1659" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1109.wmz» o:><img width=«84» height=«24» src=«dopb85039.zip» v:shapes="_x0000_i1659">, где <shape id="_x0000_i1660" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1111.wmz» o:><img width=«39» height=«19» src=«dopb84615.zip» v:shapes="_x0000_i1660">
<shape id="_x0000_i1661" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1112.wmz» o:><img width=«67» height=«24» src=«dopb85040.zip» v:shapes="_x0000_i1661">;
1) <shape id="_x0000_i1662" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1114.wmz» o:><img width=«129» height=«25» src=«dopb85041.zip» v:shapes="_x0000_i1662">
<shape id="_x0000_i1663" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1116.wmz» o:><img width=«96» height=«21» src=«dopb85042.zip» v:shapes="_x0000_i1663"> или <shape id="_x0000_i1664" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1118.wmz» o:><img width=«88» height=«41» src=«dopb85043.zip» v:shapes="_x0000_i1664">
<shape id="_x0000_i1665" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1120.wmz» o:><img width=«113» height=«21» src=«dopb85044.zip» v:shapes="_x0000_i1665">
Решаем биквадратное уравнение
Примем <shape id="_x0000_i1666" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1122.wmz» o:><img width=«47» height=«21» src=«dopb85012.zip» v:shapes="_x0000_i1666">, тогда получим <shape id="_x0000_i1667" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1123.wmz» o:><img width=«105» height=«21» src=«dopb85045.zip» v:shapes="_x0000_i1667">
D= 32 – 4*1*(-4) = 25
<shape id="_x0000_i1668" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1125.wmz» o:><img width=«75» height=«41» src=«dopb85046.zip» v:shapes="_x0000_i1668">; <shape id="_x0000_i1669" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1127.wmz» o:><img width=«52» height=«23» src=«dopb85047.zip» v:shapes="_x0000_i1669"> или <shape id="_x0000_i1670" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1129.wmz» o:><img width=«48» height=«41» src=«dopb85048.zip» v:shapes="_x0000_i1670">
а) <shape id="_x0000_i1671" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1131.wmz» o:><img width=«87» height=«26» src=«dopb85049.zip» v:shapes="_x0000_i1671">
б) <shape id="_x0000_i1672" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1133.wmz» o:><img width=«49» height=«41» src=«dopb85050.zip» v:shapes="_x0000_i1672">; <shape id="_x0000_i1673" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1135.wmz» o:><img width=«57» height=«41» src=«dopb85051.zip» v:shapes="_x0000_i1673"> (не удовлетворяет ОДЗ)
<shape id="_x0000_i1674" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1137.wmz» o:><img width=«48» height=«41» src=«dopb85052.zip» v:shapes="_x0000_i1674">
<shape id="_x0000_i1675" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1139.wmz» o:><img width=«223» height=«72» src=«dopb85053.zip» v:shapes="_x0000_i1675">
<shape id="_x0000_i1676" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1141.wmz» o:><img width=«49» height=«45» src=«dopb85054.zip» v:shapes="_x0000_i1676"> - решение системы уравнений.
2) <shape id="_x0000_i1677" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1143.wmz» o:><img width=«121» height=«25» src=«dopb85055.zip» v:shapes="_x0000_i1677">
<shape id="_x0000_i1678" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1145.wmz» o:><img width=«91» height=«21» src=«dopb85056.zip» v:shapes="_x0000_i1678">
<shape id="_x0000_i1679" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1147.wmz» o:><img width=«116» height=«21» src=«dopb85057.zip» v:shapes="_x0000_i1679">
<shape id="_x0000_i1680" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1149.wmz» o:><img width=«116» height=«24» src=«dopb85058.zip» v:shapes="_x0000_i1680">
<shape id="_x0000_i1681" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1151.wmz» o:><img width=«37» height=«19» src=«dopb84658.zip» v:shapes="_x0000_i1681"> или <shape id="_x0000_i1682" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1152.wmz» o:><img width=«100» height=«21» src=«dopb85059.zip» v:shapes="_x0000_i1682">
<shape id="_x0000_i1683" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1151.wmz» o:><img width=«37» height=«19» src=«dopb84658.zip» v:shapes="_x0000_i1683"> — (не удовлетворяет ОДЗ)
D= (-1)2 -4*4*3 = -47 – корней нет.
Ответ: <shape id="_x0000_i1684" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1154.wmz» o:><img width=«44» height=«45» src=«dopb85060.zip» v:shapes="_x0000_i1684">. [ ]
Пример № 36
<shape id="_x0000_i1685" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1156.wmz» o:><img width=«333» height=«42» src=«dopb85061.zip» v:shapes="_x0000_i1685">
Решение
Для любого х <shape id="_x0000_i1686" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1158.wmz» o:><img width=«113» height=«21» src=«dopb85062.zip» v:shapes="_x0000_i1686"> и <shape id="_x0000_i1687" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1160.wmz» o:><img width=«111» height=«21» src=«dopb85063.zip» v:shapes="_x0000_i1687"> ОДЗ этого уравнения состоит из всех х удовлетворяющих условию <shape id="_x0000_i1688" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1162.wmz» o:><img width=«65» height=«21» src=«dopb85064.zip» v:shapes="_x0000_i1688">, т.е. ОДЗ есть множество всех х из промежутка <shape id="_x0000_i1689" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1164.wmz» o:><img width=«69» height=«19» src=«dopb85065.zip» v:shapes="_x0000_i1689">на этом множестве. Исходное уравнение равносильно совокупности уравнений.
<shape id="_x0000_i1690" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1166.wmz» o:><img width=«79» height=«25» src=«dopb85066.zip» v:shapes="_x0000_i1690"> и <shape id="_x0000_i1691" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1168.wmz» o:><img width=«187» height=«21» src=«dopb85067.zip» v:shapes="_x0000_i1691">
Решаем ее.
<shape id="_x0000_i1692" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1170.wmz» o:><img width=«67» height=«21» src=«dopb85068.zip» v:shapes="_x0000_i1692"> <shape id="_x0000_i1693" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1172.wmz» o:><img width=«139» height=«27» src=«dopb85069.zip» v:shapes="_x0000_i1693">
<shape id="_x0000_i1694" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1174.wmz» o:><img width=«105» height=«23» src=«dopb85070.zip» v:shapes="_x0000_i1694"> <shape id="_x0000_i1695" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1176.wmz» o:><img width=«47» height=«21» src=«dopb85071.zip» v:shapes="_x0000_i1695">
<shape id="_x0000_i1696" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1178.wmz» o:><img width=«95» height=«23» src=«dopb85072.zip» v:shapes="_x0000_i1696"> <shape id="_x0000_i1697" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1180.wmz» o:><img width=«116» height=«41» src=«dopb85073.zip» v:shapes="_x0000_i1697">
<shape id="_x0000_i1698" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1182.wmz» o:><img width=«69» height=«19» src=«dopb85065.zip» v:shapes="_x0000_i1698"> принадлежат <shape id="_x0000_i1699" type="#_x0000_t75" o:ole=""><imagedata src=«18604.files/image1183.wmz» o:><img width=«208» height=«41» src=«dopb85074.zip» v:shapes="_x0000_i1699">. Они и являются решениями исходного уравнения.
продолжение
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