\(\Leftrightarrow\left\{{}\begin{matrix}2x-1\ge0\\\sqrt{x^2-2x+2}^2+\sqrt{2x-1}^2-2\sqrt{\left(x^2-2x+2\right)\left(2x-1\right)}\le0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge\dfrac{1}{2}\\\left(\sqrt{x^2-2x+2}-\sqrt{2x-1}\right)^2\le0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge\dfrac{1}{2}\\\sqrt{x^2-2x+2}=\sqrt{2x-1}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge\dfrac{1}{2}\\x^2-4x+3=0\end{matrix}\right.\)
\(\Rightarrow x=3\)
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