4^x+10^x-2*25^x=0 Решите уравнение. Created by olga0nels. algebra-ru

4^x+10^x-2*25^x=0 Решите уравнение...

olga0nels @olga0nels

August 2022 1 4 Report

4^x+10^x-2*25^x=0
Решите уравнение

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Dимасuk

Verified answer

4ˣ + 10ˣ - 2·25ˣ = 0
2²ˣ + 2ˣ·5ˣ - 2·5²ˣ = 0 |:5²ˣ
(2/5)²ˣ + (2/5)ˣ - 2 = 0
Пусть t = (2/5)ˣ, t > 0
t² + t - 2 = 0
t₁ + t₂ = -1
t₁t₂ = -2
t₁ = -2 - не подходит; t₂ = 1
Обратная замена:
(2/5)ˣ = 1
(2/5)ˣ = (2/5)⁰
x = 0
Ответ: x = 0.

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