ĐKXĐ: 2x^2-3x+1>=0
=>(2x-1)(x-1)>=0
=>\(\left[{}\begin{matrix}x>=1\\x< =\dfrac{1}{2}\end{matrix}\right.\)
\(\sqrt{2x^2-3x+1}=x-1\)
=>\(\left\{{}\begin{matrix}2x^2-3x+1=\left(x-1\right)^2\\x-1>=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x^2-3x+1=x^2-2x+1\\x>=1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x^2-x=0\\x>=1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x\left(x-1\right)=0\\x>=1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x\in\left\{0;1\right\}\\x>=1\end{matrix}\right.\)
=>x=1
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