Question

Решите логарифмическое неравенства lg(x^2+2x+2)<1

Answer 1

$lg(x^2+2x+2)\ \textless \ 1\; ,\; \; ODZ:\; x^2+2x+2\ \textgreater \ 0\\\\lg(x^2+2x+2)\ \textless \ lg10\\\\x^2+2x+2\ \textless \ 10\\\\x^2+2x-8\ \textless \ 0\\\\x_1=-4,\; x_2=2\; (teor.\; Vieta)\\\\+++(-4)---(2)+++\\\\x\in (-4,2)$