\(\Leftrightarrow\sqrt{\left(x-1\right)^2}+\sqrt{\left(x-2\right)^2}=3\)
\(\Leftrightarrow\left|x-1\right|+\left|x-2\right|=3\)
_Với x<1 \(\Rightarrow1-x-x+2=3\)
\(\Rightarrow3-2x=3\)
\(\Rightarrow x=0\) (t/m)
_Với \(1\le x< 2\Rightarrow x-1+2-x=3\)
\(\Rightarrow0x=2\) (Vô lý)
_Với x>2 \(\Rightarrow x-1+x-2=3\)
\(\Leftrightarrow2x=6\Leftrightarrow x=3\) (t/m)
Vậy x=0 hoặc x=6.
\(\sqrt{x^2-2x+1}+\sqrt{x^2-4x+4}=3\)
\(\Leftrightarrow\sqrt{\left(x-1\right)^2}+\sqrt{\left(x-2\right)^2}=3\)
\(\Leftrightarrow\left|x-1\right|+\left|x-2\right|=3\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1+x-2=3\\1-x+2-x=3\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-3=3\\3-2x=3\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=0\end{matrix}\right.\)
