ĐKXĐ: \(1\le x\le6\)
\(\Leftrightarrow3x^2-4x-1-\sqrt{x-1}-\sqrt{6-x}=0\)
\(\Leftrightarrow3x^2-4x-4+1-\sqrt{x-1}+2-\sqrt{6-x}=0\)
\(\Leftrightarrow\left(x-2\right)\left(3x+2\right)-\frac{x-2}{1+\sqrt{x-1}}+\frac{x-2}{2+\sqrt{6-x}}=0\)
\(\Leftrightarrow\left(x-2\right)\left(3x+2-\frac{1}{1+\sqrt{x-1}}+\frac{1}{2+\sqrt{6-x}}\right)=0\)
\(\Leftrightarrow x-2=0\) (ngoặc phía sau luôn dương)
\(\Rightarrow x=2\)
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