ĐKXĐ: \(\left\{{}\begin{matrix}2x^2-1>=0\\2x-1>=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>=\dfrac{1}{2}\\x^2>=\dfrac{1}{2}\end{matrix}\right.\Leftrightarrow x>=\dfrac{\sqrt{2}}{2}\)
PT\(\Leftrightarrow\sqrt{2x^2-1}-1+x\sqrt{2x-1}-x=2x^2-x-1\)
\(\Leftrightarrow\dfrac{2x^2-1-1}{\sqrt{2x^2-1}+1}+x\cdot\dfrac{2x-1-1}{\sqrt{2x-1}+1}=\left(x-1\right)\left(2x+1\right)\)
=>\(\dfrac{2\left(x-1\right)\left(x+1\right)}{\sqrt{2x^2-1}}+2x\cdot\dfrac{x-1}{\sqrt{2x-1}+1}-\left(x-1\right)\left(2x+1\right)=0\)
=>\(\left(x-1\right)\left(\dfrac{2x+2}{\sqrt{2x^2-1}}+\dfrac{2x}{\sqrt{x-1}+1}-2x-1\right)=0\)
=>x-1=0
=>x=1
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