\(\Delta=\left(m+1\right)^2-8\ge0\Rightarrow\left[{}\begin{matrix}m\ge-1+2\sqrt{2}\\m\le-1-2\sqrt{2}\end{matrix}\right.\)
Phương trình ko có nghiệm \(x=0\) nên biểu thức đề bài luôn xác định
Theo Viet: \(\left\{{}\begin{matrix}x_1+x_2=m+1\\x_1x_2=2\end{matrix}\right.\)
\(\left(\frac{x_1}{x_2}\right)^2+\left(\frac{x_2}{x_1}\right)^2=14\)
\(\Leftrightarrow\left(\frac{x_1}{x_2}+\frac{x_2}{x_1}\right)^2=16\)
\(\Leftrightarrow\left(\frac{x_1^2+x_2^2}{x_1x_2}\right)^2=16\Leftrightarrow\left(\frac{x_1^2+x_2^2}{2}\right)^2=16\)
\(\Leftrightarrow\frac{x_1^2+x_2^2}{2}=4\Leftrightarrow\left(x_1+x_2\right)^2-2x_1x_2=8\)
\(\Leftrightarrow\left(m-1\right)^2=12\Leftrightarrow\left[{}\begin{matrix}m=1+2\sqrt{3}\\m=1-2\sqrt{3}\left(l\right)\end{matrix}\right.\)