$\sqrt{x^{2}-2x+5}=x-2$
$\Leftrightarrow$ $x^{2}-2x+5=x^{2}-4x+4$
$\Leftrightarrow$ $-2x+5=-4x+4$
$\Leftrightarrow$ $-2x+4x=4-5$
$\Leftrightarrow$$2x=-1$
$\Leftrightarrow$ $x=$ $\dfrac{-1}{2}$
Kiểm tra nghiệm của PT, ta được:
$\sqrt{(\dfrac{-1}{2})^{2}-2.(\dfrac{-1}{2})+5}=\dfrac{-1}{2}-2$$\\$$\rightarrow$ $\dfrac{5}{2}\ne \dfrac{-5}{2}$$\\$$\Rightarrow$ $x\ne$ $\dfrac{-1}{2}$
Vậy `x` $\in$ $\emptyset$
