\(\sqrt{x-2x^2+1}>1-x\)
TH1: \(1-x\ge0\Rightarrow x\le1\)
\(\sqrt{x-2x^2+1}>1-x\\ \Leftrightarrow x-2x^2+1>x^2-2x+1\\ \Leftrightarrow-2x^2>-2x\\ \Leftrightarrow-2x^2+2x>0\\ \Leftrightarrow-2x\left(x-1\right)>0\\ \Leftrightarrow x\left(x-1\right)< 0\\ \Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 0\\x-1>0\end{matrix}\right.\\\left\{{}\begin{matrix}x>0\\x-1< 0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 0\\x>1\end{matrix}\right.\\\left\{{}\begin{matrix}x>0\\x< 1\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x\in\varnothing\\x\in\left(0;1\right)\end{matrix}\right.\)
TH2: \(1-x< 0\Leftrightarrow x>1\)
Tương tự ........
