Системи неравенства

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[ammornil]

[tex]\begin{aligned} \begin{array}{|l} \frac{\normalsize{3x^{2}-7x+8}}{\normalsize{x^{2}+1}}>1 \\ \frac{\normalsize{3x^{2}-7x+8}}{\normalsize{x^{2}+1}}<2 \end{array} \\ & \text{ДМ: } \forall x \in \mathbb{R} \\ \begin{array}{|l} 3x^{2}-7x+8-x^{2}-1>0 \\ 3x^{2}-7x+8-2x^{2}-2<0 \end{array} \Leftrightarrow \begin{array}{|l} 2x^{2}-7x+7>0 \\ x^{2}-7x+6<0 \end{array} \Leftrightarrow \begin{array}{|l} \begin{array}{|l} 2>0 \\ D<0 \end{array} \Rightarrow \forall x \in \mathbb{R} \\ (x-1)(x-6)<0 \end{array} \Rightarrow \end{aligned}[/tex]$$ x \in (1;6) $$