\(x^2-4x-3\left|x+2\right|+4=0\Leftrightarrow\left(x^2-4x+4\right)=3\left|x+2\right|\Leftrightarrow\left(x+2\right)^2=3\left|x+2\right|\)
\(+,x\ge-2\Rightarrow x+2\ge0\Rightarrow\left|x+2\right|=x+2\Rightarrow\left(x+2\right)^2=3\left(x+2\right)\Leftrightarrow\left(x+2\right)\left(x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x+2=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=1\end{matrix}\right.\left(thoaman\right)\)
\(+,x< -2\Rightarrow x+2< 0\Rightarrow\left|x+2\right|=-\left(x+2\right)\Rightarrow\left(x+2\right)^2=-3\left(x+2\right)\Leftrightarrow\left(x+2\right)\left(x+5\right)=0\Leftrightarrow\left[{}\begin{matrix}x+2=0\\x+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-2\left(loai\right)\\x=-5\left(thoaman\right)\end{matrix}\right.\)
\(Vay:x\in\left\{-5;-2;1\right\}\)
