ĐKXĐ: \(-4\le x\le6\)
\(\Leftrightarrow\left(\sqrt{x+4}+2\right)^2\left(\sqrt{6-x}+x-5\right)=\left(\sqrt{x+4}+2\right)^2\left(\sqrt{x+4}-2\right)^2\)
\(\Leftrightarrow\sqrt{6-x}+x-5=\left(\sqrt{x+4}-2\right)^2\)
\(\Leftrightarrow\sqrt{6-x}+x-5=x+8-4\sqrt{x+4}\)
\(\Leftrightarrow\sqrt{6-x}+4\sqrt{x+4}=13\)
\(\Leftrightarrow15x+70+8\sqrt{-x^2+2x+24}=169\)
\(\Leftrightarrow8\sqrt{-x^2+2x+24}=99-15x\) \(\left(x\le\frac{33}{5}\right)\)
\(\Leftrightarrow64\left(-x^2+2x+24\right)=\left(99-15x\right)^2\)
\(\Leftrightarrow289x^2-3098x+8265=0\Rightarrow\left[{}\begin{matrix}x=5\\x=\frac{1653}{289}\end{matrix}\right.\)
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