Question

помагите решить

log0.5(x+2)+log0.5(x+3)=log0.5(3-1)

Answer 1

ОДЗ:
x + 2 > 0
x + 3 > 0
x > -3
x > -2

$log_{0,5}(x + 2)(x + 3) = log_{0,5}2 \ \ (x + 2)(x + 3) = 2 \ \ x^2 + 2x + 3x + 6 = 2\ \ x^2 + 5x + 4 = 0 \ \ x_1 + x_2 = -5 \ x_1 cdot x_2 = 4 \ \ x_1 = -1 \ x_2 = -4 - ne ud.$

Ответ: x = -1.