ĐKXĐ: \(x=2\)
\(pt\Leftrightarrow2x+2\sqrt{x-2}=2\sqrt{2-x}+4\)
\(\Leftrightarrow x-2+2\sqrt{x-2}+1=2-x+2\sqrt{2-x}+1\)
\(\Leftrightarrow\left(\sqrt{x-2}+1\right)^2=\left(\sqrt{2-x}+1\right)^2\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x-2}+1=\sqrt{2-x}+1\\\sqrt{x-2}+1=-\sqrt{2-x}-1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x-2}=\sqrt{2-x}\\2\sqrt{x-2}=-2\left(\text{vô nghiệm}\right)\end{matrix}\right.\Leftrightarrow x=2\left(tm\right)\)