Question

giải phương trình  |x^2 - 2x -1|== x-1

Answer 1

\(\Leftrightarrow\left[{}\begin{matrix}x^2-2x-1=x-1\\x-1>=0\end{matrix}\right.\Leftrightarrow x=3\)

Answer 2

\(\Leftrightarrow\left[{}\begin{matrix}x^2-2x-1=x-1\left(x\le1-\sqrt{2};x\ge1+\sqrt{2}\right)\\x^2-2x-1=1-x\left(1-\sqrt{x}< x< 1+\sqrt{2}\right)\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=0\left(ktm\right);x=3\left(tm\right)\\x=-1\left(ktm\right);x=2\left(tm\right)\end{matrix}\right.\)