Question

giải phương trình : |2x-1|=x^2 -2x-5

Answer 1

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}2x-1\ge0\\2x-1=x^2-2x-5\end{matrix}\right.\\\left\{{}\begin{matrix}2x-1\le0\\2x-1=x^2-2x-5\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge\dfrac{1}{2}\\x^2-4x-4=0\end{matrix}\right.\\\left\{{}\begin{matrix}x\le\dfrac{1}{2}\\x^2=4\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=2+2\sqrt{2}\\x=-2\end{matrix}\right.\)