\(\sqrt{x^2-4}+\sqrt{x+2}=0\) (ĐK: \(x\ge2\))
\(\Leftrightarrow\sqrt{\left(x+2\right)\left(x-2\right)}+\sqrt{x+2}=0\)
\(\Leftrightarrow\sqrt{x+2}\left(\sqrt{x-2}+1\right)=0\)
\(\Leftrightarrow\sqrt{x+2}=0\)
\(\Leftrightarrow x+2=0\)
\(\Leftrightarrow\text{x}=-2\left(ktm\right)\)
\(\sqrt[]{x^2-4}+\sqrt[]{x+2}=0\left(x\ge2\right)\)
\(\Leftrightarrow\sqrt[]{\left(x+2\right)\left(x-2\right)}+\sqrt[]{x+2}=0\)
\(\Leftrightarrow\sqrt[]{x+2}\left(\sqrt[]{\left(x-2\right)}+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt[]{x+2}=0\\\sqrt[]{\left(x-2\right)}+1=0\left(đúng,\forall x\ge2\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x+2=0\\x\ge2\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=-2\\x\ge2\end{matrix}\right.\)
\(...\left[{}\begin{matrix}x=-2\left(loại\right)\\x\ge2\end{matrix}\right.\) \(\Leftrightarrow x\ge2\)
\(\sqrt{x^2-4}+\sqrt{x+2}=0\\ \Leftrightarrow\sqrt{\left(x-2\right).\left(x+2\right)}+\sqrt{x+2}=0\\ \Leftrightarrow\sqrt{x-2}\sqrt{x+2}+\sqrt{x+2}=0\\ \Leftrightarrow\sqrt{x+2}\left(\sqrt{x-2}+1\right)=0\\ \Rightarrow\left[{}\begin{matrix}\sqrt{x+2}=0\\\sqrt{x-2}+1=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x+2=0\\x-2+1=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=-2\\x-1=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=-2\\x=1\end{matrix}\right.\)
Loại x=1
