Question

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

Answer 1

Ta có:\(\sqrt{x^2-4x+4}=-x+4\)

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

     \(\Leftrightarrow\left|x-2\right|=-x+4\)

     \(\Leftrightarrow\left[{}\begin{matrix}x-2=-x+4\\x-2=x-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=6\\0=-2\left(loại\right)\end{matrix}\right.\Leftrightarrow x=3\)

Answer 2

ĐK:\(x\ge2\)

Answer 3

Ta có: \(\sqrt{x^2-4x+4}=-x+4\)

\(\Leftrightarrow\left|x-2\right|=4-x\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2=4-x\left(x\ge2\right)\\x-2=x-4\left(x< 2\right)\left(loại\right)\end{matrix}\right.\Leftrightarrow x+x=4+2\)

\(\Leftrightarrow2x=6\)

hay x=3(nhận)