\(\sqrt{x^2-4}+\sqrt{x+2}=0\\ \Leftrightarrow\sqrt{\left(x-2\right).\left(x+2\right)}+\sqrt{x+2}=0\\ \Leftrightarrow\sqrt{x-2}\sqrt{x+2}+\sqrt{x+2}=0\\ \Leftrightarrow\sqrt{x+2}\left(\sqrt{x-2}+1\right)=0\\ \Rightarrow\left[{}\begin{matrix}\sqrt{x+2}=0\\\sqrt{x-2}+1=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x+2=0\\x-2+1=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=-2\\x-1=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=-2\\x=1\end{matrix}\right.\)

Loại x=1