\(\sqrt{x-\sqrt{2x-1}}=\sqrt{2}\left(x\ge\dfrac{1}{2}\right)\)
\(\Leftrightarrow\sqrt{2x-2\sqrt{2x-1}}=2\)
\(\Leftrightarrow\sqrt{2x-1-2\sqrt{2x-1}+1}=2\)
\(\Leftrightarrow\sqrt{\left(\sqrt{2x-1}-1\right)^2}=2\)
\(\Leftrightarrow\sqrt{2x-1}-1=2\)
\(\Leftrightarrow\sqrt{2x-1}=3\)
\(\Leftrightarrow2x-1=9\)
\(\Leftrightarrow2x=10\)
\(\Leftrightarrow x=5\left(TM\right)\)
Vậy PT có nghiệm là \(x=5\)
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