[latex]log_{1/2} (x^{2}+7x+10 ) больше -2[/latex]

[latex]log_{\frac{1}{2}}(x^2+7x+10)>-2,\quad ODZ:\; x^2+7x+10>0\\\\Po\; teor.\; Vieta:\; x_1=-2,x_2=-5\\\\+ + + +(-5)- - - -(-2)+ + + + +\\\\x\in (-\infty,-5)U(-2,+\infty)\; -\; ODZ\\\\x^2+7x+10<(\frac{1}{2})^{-2}\\\\(\frac{1}{2})^{-2}=4\\\\x^2+7x+6<0\\\\x_1=-6,x_2=-1[/latex] [latex]x\in (-6,-1)\\\\------(-6)////(-5)--------(-2)/////(-1)----\\\\Otvet:\; x\in (-6,-5)U(-2,-1)[/latex]