ĐK: \(1\le x\le2\)
\(PT\Leftrightarrow\left(\sqrt{x-1}+\sqrt{2-x}\right)^2=1\) và \(\sqrt{x-1}+\sqrt{2-x}\ge0\)
\(\Leftrightarrow\sqrt{x-1}+\sqrt{2-x}=1\)
\(\Leftrightarrow1+2\sqrt{\left(x-1\right)\left(2-x\right)}=1\)
\(\Leftrightarrow\sqrt{\left(x-1\right)\left(2-x\right)}=0\Rightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\) (tm)