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OVI1320
@OVI1320
August 2022
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решить уравнение
2*3^(-2x+2)=3^(-x+1)+1
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Dимасuk
Verified answer
2·3^(-2x + 2) = 3^(-x + 1) + 1
Пусть t = 3^(-x + 1), t > 0.
2t² = t + 1
2t² - t - 1 = 0
2t² - 2t + t - 1 = 0
2t(t - 1) + (t - 1) = 0
(2t + 1)(t - 1) = 0
2t = -1 или t - 1 = 0
t = -1/2 - пост. корень t = 1
Обратная замена:
3^(-x + 1) = 1
3^(-x + 1) = 3⁰
-x + 1 = 0
-x = -1
x = 1
Ответ: x = 1.
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Answers & Comments
Verified answer
2·3^(-2x + 2) = 3^(-x + 1) + 1Пусть t = 3^(-x + 1), t > 0.
2t² = t + 1
2t² - t - 1 = 0
2t² - 2t + t - 1 = 0
2t(t - 1) + (t - 1) = 0
(2t + 1)(t - 1) = 0
2t = -1 или t - 1 = 0
t = -1/2 - пост. корень t = 1
Обратная замена:
3^(-x + 1) = 1
3^(-x + 1) = 3⁰
-x + 1 = 0
-x = -1
x = 1
Ответ: x = 1.