\(x\ge-3\)
\(\sqrt{x+3}=4x^2+4x+1+x-2\)
Đặt \(\sqrt{x+3}=a\ge0\Rightarrow a^2=x+3\)
\(\Leftrightarrow\left(2x+1\right)^2+x-2=a\)
\(\Leftrightarrow\left(2x+1\right)^2-a^2+a^2+x-2-a=0\)
\(\Leftrightarrow\left(2x+1-a\right)\left(2x+1+a\right)+2x+1-a=0\)
\(\Leftrightarrow\left(2x+1-a\right)\left(2x+2+a\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x+1=a\\-2x-2=a\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}2x+1=\sqrt{x+3}\left(1\right)\\-2x-2=\sqrt{x+3}\left(2\right)\end{matrix}\right.\)
- Xét (1) \(\Leftrightarrow\left\{{}\begin{matrix}2x+1\ge0\\\left(2x+1\right)^2=x+3\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ge-\frac{1}{2}\\4x^2+3x-2=0\end{matrix}\right.\) \(\Rightarrow x=\frac{-3+\sqrt{41}}{8}\)
- Xét (2)\(\Leftrightarrow\left\{{}\begin{matrix}-2x-2\ge0\\\left(-2x-2\right)^2=x+3\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\le-1\\4x^2+7x+1=0\end{matrix}\right.\) \(\Rightarrow x=\frac{-7-\sqrt{33}}{8}\)
