\(\Leftrightarrow6-2x=\sqrt{x+6}-3\sqrt{x-2}.\) Bình phương 2 vế
\(\Rightarrow\left(6-2x\right)^2=\left(\sqrt{x+6}-3\sqrt{x-2}\right)^2\Rightarrow36-24x+4x^2=x+6+9x-18-6\sqrt{(x+6)\left(x-2\right)}\Rightarrow4x^2-34x+48=-6\sqrt{\left(x+6\right)\left(x-2\right)}\Rightarrow2x^2-17x+24=-3\sqrt{\left(x+6\right)\left(x-2\right)}\)Bình p 2 vế\(\Rightarrow4x^4-68x^3+289x^2-816x+96x^2+576=9\left(x^2+4x-12\right)\)
\(\Rightarrow4x^4-68x^3+376x^2-852x+684=0\)
\(\Rightarrow\)\(\left[{}\begin{matrix}x=3\\x=\frac{11-3\sqrt{5}}{2}\\x=\frac{11+3\sqrt{5}}{2}\end{matrix}\right.\)
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