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lesnsh
@lesnsh
July 2022
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Помогите пожалуйста .....
Решите уравнение: 7*49^х = 50*7^х -7
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nelle987
Verified answer
7 * (7^x)^2 = 50 * 7^x - 7
Вводим новую переменную t = 7^x, t > 0. Получается квадратное уравнение относительно t:
7t^2 = 50t - 7
7t^2 - 50t + 7 = 0
D/4 = 25^2 - 7^2 = (25 - 7)(25 + 7) = 18 * 32 = 9 * 64 = 24^2
t = (25 +- 24)/7
t = 7 или t = 1/7
7^x = 7 или 7^x = 1/7
x = 1 или x = -1
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Answers & Comments
Verified answer
7 * (7^x)^2 = 50 * 7^x - 7Вводим новую переменную t = 7^x, t > 0. Получается квадратное уравнение относительно t:
7t^2 = 50t - 7
7t^2 - 50t + 7 = 0
D/4 = 25^2 - 7^2 = (25 - 7)(25 + 7) = 18 * 32 = 9 * 64 = 24^2
t = (25 +- 24)/7
t = 7 или t = 1/7
7^x = 7 или 7^x = 1/7
x = 1 или x = -1