Question

\(\sqrt{x^2-2x+4}=2x-2\)

Answer 1

\(\Leftrightarrow\left\{{}\begin{matrix}4x^2-8x+4-x^2+2x-4=0\\x>=1\end{matrix}\right.\Leftrightarrow x=2\)

Answer 2

ĐKXĐ:\(\left\{{}\begin{matrix}x^2-2x+4\ge0\\2x-2\ge0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left(x-1\right)^2+3\ge0\left(luôn.đúng\right)\\x\ge1\end{matrix}\right.\Leftrightarrow x\ge1\)

\(\sqrt{x^2-2x+4}=2x-2\\ \Leftrightarrow x^2-2x+4=4x^2-8x+4\\ \Leftrightarrow3x^2-6x=0\\ \Leftrightarrow3x\left(x-2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\left(ktm\right)\\x=2\left(tm\right)\end{matrix}\right.\)