Решите уравнение log₂ (2-x) - log₂ x = log₂ x - 2

log₂ (2 - x) - log₂ x = log₂ x - 2;

log₂ (2 - x) - log₂ x = log₂ x - 2 * log₂ 2;

log₂ ((2 - x) / x) = log₂ x - log₂ 2^2;

log₂ ((2 - x) / x) = log₂ (x/4);

(2 - x) / x = x/4;

x^2 = 4 * (2 - x);

x^2 = 8 - 4 * x;

x^2 + 4 * x - 8 = 0;

D = 16 - 4 * 1 * (-8) = 16 + 48 = 64;

x1 = (-4 + 8) / 2 = 4/2 = 2;

x2 = (-4 - 8) / 2 = - 12/2 = - 6;

Ответ: х = 2 и х = - 6.