Решите неравенство[latex] 2^{x} *5^{x}\ \textless \ 10^{ x^{2} } *0,01[/latex]

[latex]2^x*5^x\ \textless \ 10^{ x^{2} } *0.01[/latex] [latex]10^x\ \textless \ 10^{ x^{2} } * 10^{-2} [/latex] [latex]10^x\ \textless \ 10^{ x^{2}-2 } [/latex] [latex]x\ \textless \ x^{2} -2[/latex] [latex]x- x^{2}+2\ \textless \ 0[/latex] [latex] x^{2} -x-2\ \textgreater \ 0[/latex] [latex]D=(-1)^2-4*1*(-2)=9[/latex] [latex]x_1= \frac{1+3}{2} =2[/latex] [latex]x_1= \frac{1-3}{2} =-1[/latex]           +                   -                     +    ------------(-1)-----------------(2)------------- /////////////                         //////////////// [latex]x[/latex] ∈ [latex](-[/latex] ∞ [latex];-1)[/latex] ∪ [latex](2;+[/latex] ∞ [latex])[/latex]