\(\left[{}\begin{matrix}\left\{{}\begin{matrix}x^2-3x+2\ge0\\x^2-3x+2+x^2>2x\end{matrix}\right.\\\left\{{}\begin{matrix}x^2-3x+2< 0\\-\left(x^2-3x+2\right)+x^2>2x\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\in(-\infty;1]\cup[2;+\infty)\\2x^2-5x+2>0\end{matrix}\right.\\\left\{{}\begin{matrix}x\in\left(1;2\right)\\x-2>0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\in(-\infty;1]\cup[2;+\infty)\\x\in(-\infty;\dfrac{1}{2})\cup(2;+\infty)\end{matrix}\right.\\\left\{{}\begin{matrix}x\in\left(1;2\right)\\x>2\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow x\in(-\infty;\dfrac{1}{2})\cup(2;+\infty)\)
