Question

Решить неравенство: lg(x^2+5x+7)<0

Answer 1

$\lg(x^2+5x+7)\ \textless \ 0\\ 0\ \textless \ x^2+5x+7\ \textless \ 1\\ \\ 1.\\ x^2+5x+7=x^2+2*2.5*x+2.5^2-2.5^2+7=\\ =(x+2.5)^2+0.75\ \textgreater \ 0 (\forall x)\\\\ 2.\\ x^2+5x+7\ \textless \ 1\\ x^2+5x+6\ \textless \ 0\\ (x+2)(x+3)\ \textless \ 0\\ x \in (2;3)$