Question

\(\sqrt{x+8}+\dfrac{9}{\sqrt{x+8}}=6\sqrt{x}\)

Answer 1

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

=>\(\left[{}\begin{matrix}x=-\dfrac{289}{35}\left(loại\right)\\x=1\left(nhận\right)\end{matrix}\right.\)

Answer 2

ĐKXĐ: \(x\ge0\)

\(\Leftrightarrow x+8+9=6\sqrt{x\left(x+8\right)}\)

\(\Leftrightarrow x+17=6\sqrt{x^2+8x}\)

\(\Leftrightarrow\left(x+17\right)^2=36\left(x^2+8x\right)\)

\(\Leftrightarrow35x^2+254x-289=0\)

\(\Rightarrow\left[{}\begin{matrix}x=1\\x=-\dfrac{289}{35}< 0\left(loại\right)\end{matrix}\right.\)