ĐKXĐ: \(-1\le x\le4\)
\(pt\Leftrightarrow\dfrac{x+1-4\left(4-x\right)}{\sqrt{x+1}+2\sqrt{4-x}}=\dfrac{5\left(x-3\right)}{\sqrt{2x^2+18}}\)
\(\Leftrightarrow\dfrac{5\left(x-3\right)}{\sqrt{x+1}+2\sqrt{4-x}}=\dfrac{5\left(x-3\right)}{\sqrt{2x^2+18}}\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\\sqrt{x+1}+2\sqrt{4-x}=\sqrt{2x^2+18}\left(1\right)\end{matrix}\right.\)
Xét (1):
\(\Leftrightarrow x+1+4\left(4-x\right)+4\sqrt{\left(x+1\right)\left(4-x\right)}=2x^2+18\)
\(\Leftrightarrow2x^2+3x+1-4\sqrt{-x^2+3x+4}=0\)
\(\Leftrightarrow2x^2-x-3+4\left(x+1-\sqrt{-x^2+3x+4}\right)=0\)
\(\Leftrightarrow2x^2-x-3+\dfrac{4\left(2x^2-x-3\right)}{x+1+\sqrt{-x^2+3x+4}}=0\)
\(\Leftrightarrow2x^2-x-3=0\)
