ĐKXĐ : \(x^2-7\ge0\Leftrightarrow\left(x-\sqrt{7}\right)\left(x+\sqrt{7}\right)\ge0\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-\sqrt{7}\ge0\\x+\sqrt{7}\ge0\end{matrix}\right.\\\left\{{}\begin{matrix}x-\sqrt{7}\le0\\x+\sqrt{7}\le0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge\sqrt{7}\\x\ge-\sqrt{7}\end{matrix}\right.\\\left\{{}\begin{matrix}x\le\sqrt{7}\\x\le-\sqrt{7}\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x\ge\sqrt{7}\\x\le-\sqrt{7}\end{matrix}\right.\)
Để biểu thức \(\sqrt{x^2-7}\) xác định thì \(x^2-7\ge0\Leftrightarrow x^2\ge7\Leftrightarrow\)\(\left[{}\begin{matrix}x\ge\sqrt{7}\\x\le-\sqrt{7}\end{matrix}\right.\)
