\(\Delta=m^2-4\ge0\Rightarrow\left\{{}\begin{matrix}m\ge2\\m\le-2\end{matrix}\right.\)
\(\left\{{}\begin{matrix}x_1x_2=1\\x_1+x_2=-m\end{matrix}\right.\)
\(\frac{x_1^2}{x_2^2}+\frac{x_2^2}{x_1^2}>7\)
\(\Leftrightarrow\left(\frac{x_1}{x_2}+\frac{x_2}{x_1}\right)^2>9\)
\(\Leftrightarrow\left[{}\begin{matrix}\frac{x_1}{x_2}+\frac{x_2}{x_1}>3\\\frac{x_1}{x_2}+\frac{x_2}{x_1}< -3\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x_1^2+x_2^2>3\\x_1^2+x_2^2< -3\left(vn\right)\end{matrix}\right.\)
\(\Leftrightarrow\left(x_1+x_2\right)^2-2x_1x_2>3\)
\(\Leftrightarrow m^2-2>3\)
\(\Leftrightarrow\left[{}\begin{matrix}m>\sqrt{5}\\m< -\sqrt{5}\end{matrix}\right.\)
