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\(\Leftrightarrow\sqrt{3x^2+5x-1}=\sqrt{x^2-x-2}+2\sqrt{2x-1}\)
\(\Leftrightarrow3x^2+5x-1=x^2+7x-6+4\sqrt{\left(x^2-x-2\right)\left(2x-1\right)}\)
\(\Leftrightarrow2x^2-2x+5=4\sqrt{\left(x+1\right)\left(x-2\right)\left(2x-1\right)}\)
\(\Leftrightarrow2x^2-2x+5=4\sqrt{\left(x+1\right)\left(2x^2-5x+2\right)}\)
Đặt \(\left\{{}\begin{matrix}\sqrt{x+1}=a\\\sqrt{2x^2-5x+2}=b\end{matrix}\right.\) \(\Rightarrow3a^2+b^2=2x^2-2x+5\)
\(3a^2+b^2=4ab\)
\(\Leftrightarrow\left(a-b\right)\left(3a-b\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}a=b\\b=3a\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x+1}=\sqrt{2x^2-5x+2}\\\sqrt{2x^2-5x+2}=3\sqrt{x+1}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2x^2-6x+1=0\\2x^2-14x-7=0\end{matrix}\right.\)
