[latex] \frac{3}{(2^{2-x^2} -1)^2} - \frac{4}{2^{2-x^2}-1} +1 \geq 0[/latex]

[latex] \frac{3}{( 2^{2- x^{2} }-1 ) ^{2} } - \frac{4}{ 2^{2- x^{2} }-1 } +1 \geq 0[/latex] ОДЗ: [latex] 2^{2- x^{2} } -1 \neq 0 2^{2- x^{2} } \neq 1 2^{2- x^{2} } \neq 2^{0} [/latex] 2-x²≠0. x≠+-√2 замена переменной: [latex] 2^{2- x^{2} } -1=t, t\ \textgreater \ 0[/latex] [latex] \frac{3}{ t^{2} } - \frac{4}{t} +1 \leq 0, \frac{3-4t+ t^{2} }{ t^{2} } \leq 0 \left \{ {{t ^{2}\ \textgreater \ 0 } \atop { t^{2} -4t+3 \leq 0}} \right. [/latex] t²-4t+3=0. t₁=3, t₂=1       +                 -            + ------------[1]----------[3]------------>t t≥1. t≤3 t²>0. t<0, t>0 / / / / / / / /    / / / / / / / / / / / / / /  / / / / /  ------------(0)--------[1]---------[3]-------------------->t                                \ \ \ \ \ \ \ \ обратная замена: t≥1. [latex] 2^{2- x^{2} }-1 \geq 1 2^{2- x^{2} } \geq 2^{1} 2- x^{2} \geq 1[/latex] (1-x)*(1+x)≥0 -1≤x≤1 t≤3 [latex] 2^{2- x^{2} } -1 \leq 3 2^{2- x^{2} } \leq 2^{2} [/latex] 2-x²≤2, -x²≤0  нет решений. x∈[-1;1]