28 tháng 8 2021 lúc 23:20
ĐK: \(x\ge1\)
\(\sqrt{5x+3}-\sqrt{x-1}=\sqrt{3x-1}\)
\(\Leftrightarrow\sqrt{5x+3}=\sqrt{x-1}+\sqrt{3x-1}\)
\(\Leftrightarrow5x+3=x-1+3x-1+2\sqrt{\left(3x-1\right)\left(x-1\right)}\)
\(\Leftrightarrow2\sqrt{3x^2-4x+1}=x+\text{}5\)
\(\Leftrightarrow4\left(3x^2-4x+1\right)=\left(x+5\right)^2\)
\(\Leftrightarrow11x^2-26x-21=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\left(tm\right)\\x=-\dfrac{7}{11}\left(l\right)\end{matrix}\right.\)
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