Question

Показательное уравнение( плиз Алгебра 10 класс

Answer 1

$3*2^{\frac{x-1}{\sqrt x + 1}} - 8*2^{\frac{\sqrt x - 1}2} + 4 = 0\\\frac{x-1}{\sqrt x + 1} = \frac{(x-1)(\sqrt x - 1)}{(\sqrt x + 1)(\sqrt x - 1)} = \frac{(x-1)(\sqrt x - 1)}{x-1} = \sqrt x - 1\\2^{\frac{x-1}{\sqrt x + 1}} = 2^{\sqrt x - 1}\\3*2^{\sqrt x - 1} - 8*2^{\frac{\sqrt x - 1}2} + 4 = 0\\2^{\frac{\sqrt x - 1}2} = t\\3*t^2 - 8*t + 4 = 0\\D = 64 - 48 = 16\\t_1 = \frac{8 + 4}6 = 2\\t_2 = \frac{8 - 4}6 = \frac23\\1) 2^{\frac{\sqrt x - 1}2} = 2^1\\\frac{\sqrt x - 1}2 = 1\\\sqrt x = 3\\x = 9$

$2)2^{ \frac{\sqrt x - 1}2} = \frac23\\\frac{\sqrt x - 1}2 = log_2\frac23\\\sqrt x - 1 = 2*log_2\frac23\\\sqrt x = 3 - log_29\\x = (3-log_29)^2$