ĐKXĐ: x>=0
\(\sqrt{x+8}+\dfrac{9}{\sqrt{x+8}}=6\sqrt{x}\)
=>\(\dfrac{x+8+9}{\sqrt{x+8}}=\sqrt{36x}\)
=>\(\sqrt{36x\left(x+8\right)}=x+17\)
=>\(36x\left(x+8\right)=\left(x+17\right)^2\)
=>\(36x^2+288x=x^2+34x+289\)
=>\(35x^2+254x-289=0\)
=>\(35x^2+289x-35x-289=0\)
=>(35x+289)(x-1)=0
=>\(\left[{}\begin{matrix}x=-\dfrac{289}{35}\left(loại\right)\\x=1\left(nhận\right)\end{matrix}\right.\)
ĐKXĐ: \(x\ge0\)
\(\Leftrightarrow x+8+9=6\sqrt{x\left(x+8\right)}\)
\(\Leftrightarrow x+17=6\sqrt{x^2+8x}\)
\(\Leftrightarrow\left(x+17\right)^2=36\left(x^2+8x\right)\)
\(\Leftrightarrow35x^2+254x-289=0\)
\(\Rightarrow\left[{}\begin{matrix}x=1\\x=-\dfrac{289}{35}< 0\left(loại\right)\end{matrix}\right.\)
