Решите уравнение: [tex] \frac{ 3^{x}- 3^{-x} }{3^{x}+ 3^{-x}} = \frac{4}{5} [/tex]. Created by SabiB. algebra-ru

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ОДЗ:
3ˣ ≠ -3⁻ˣ
x ∈ R

5·3ˣ - 5·3⁻ˣ = 4·3ˣ + 4·3⁻ˣ
5·3ˣ - 4·3ˣ = 4·3⁻ˣ + 5·3⁻ˣ
3ˣ = 9·3⁻ˣ
3ˣ = 3⁻ˣ⁺²
x = -x + 2
x + x = 2
2x = 2
x = 1
Ответ: x = 1.

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