ĐKXĐ: ...
\(\Leftrightarrow x^2+5x+8=3\sqrt{\left(2x+3\right)\left(x^2+x+2\right)}\)
Đặt \(\left\{{}\begin{matrix}\sqrt{2x+3}=a\\\sqrt{x^2+x+2}=b\end{matrix}\right.\)
\(\Rightarrow2a^2+b^2=3ab\Leftrightarrow2a^2-3ab+b^2=0\)
\(\Leftrightarrow\left(a-b\right)\left(2a-b\right)=0\Rightarrow\left[{}\begin{matrix}a=b\\b=2a\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{2x+3}=\sqrt{x^2+x+2}\\2\sqrt{2x+3}=\sqrt{x^2+x+2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2+x+2=2x+3\\x^2+x+2=8x+12\end{matrix}\right.\)
