ĐK : \(x\ge1\) . Bình phương 2 vế ta được :
\(5x-1+3x-2-2\sqrt{\left(5x-1\right)\left(3x-2\right)}=x-1\)
\(\Leftrightarrow-2\sqrt{\left(5x-1\right)\left(3x-2\right)}=-7x+2\)
\(\Leftrightarrow\sqrt{\left(5x-1\right)\left(3x-2\right)}=\dfrac{7x-2}{2}\)
\(\Leftrightarrow15x^2-13x+2=\dfrac{49x^2-28x+4}{4}\)
\(\Leftrightarrow60x^2-52x+8-49x^2+28x-4=0\)
\(\Leftrightarrow11x^2-24x+4=0\)
\(\Delta=\left(-24\right)^2-4.4.11=400\)
\(\Rightarrow\left\{{}\begin{matrix}x_1=\dfrac{24+\sqrt{400}}{22}=2\left(TM\right)\\x_2=\dfrac{24-\sqrt{400}}{22}=\dfrac{2}{11}\left(KTM\right)\end{matrix}\right.\)
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