Log7(x в степени2 +3x)>1

1" alt="log_7 (x^2+2x)>1" align="absmiddle" class="latex-formula">

0" alt="x^2+2x>0" align="absmiddle" class="latex-formula">

0" alt="x(x+2)>0" align="absmiddle" class="latex-formula">
x є $(-\infty;-2) \cup (0;+\infty)$

1; x^2+2x>7^1" alt="7>1; x^2+2x>7^1" align="absmiddle" class="latex-formula">

7>0" alt="x^2+2x>7>0" align="absmiddle" class="latex-formula">

0" alt="x^2+2x-7>0" align="absmiddle" class="latex-formula">

0" alt="a=1>0" align="absmiddle" class="latex-formula"> - ветви параболы направлены верх
$D=2^2-4*1*(-7)=32=16*2=4^2*2$
$x_1=\frac{-2-4\sqrt{2}}{2*1}=-2-2\sqrt{2}$
$x_2=-2+2\sqrt{2}$
х є $(-\infty;-2-2\sqrt{2}) \cup (-2+2\sqrt{2})$