\(\sqrt{x+8}-\sqrt{5x+20}+2=0\left(đk:x\ge-4\right)\)
\(\Leftrightarrow\sqrt{x+8}=\sqrt{5x+20}-2\)
\(\Leftrightarrow x+8=5x+20+4-4\sqrt{5x+20}\)
\(\Leftrightarrow4x+16=4\sqrt{5x+20}\)
\(\Leftrightarrow x^2+8x+16=5x+20\)
\(\Leftrightarrow x^2+3x-4=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\left(tm\right)\\x=-4\left(tm\right)\end{matrix}\right.\)
ĐKXĐ: \(x\ge4\)
\(\sqrt{x+8}+2=\sqrt{5x+20}\)
\(\Leftrightarrow x+12+4\sqrt{x+8}=5x+20\)
\(\Leftrightarrow\sqrt{x+8}=x+2\) (\(x\ge-2\))
\(\Rightarrow x+8=x^2+4x+4\)
\(\Rightarrow x^2+3x-4=0\Rightarrow\left[{}\begin{matrix}x=1\\x=-4< -2\left(loại\right)\end{matrix}\right.\)
