已知 $\left(m^2+\frac{1}{m^2}-4\right)^2=36$，求 $m-\frac{1}{m}$ 的值
【答案】 解：
$\left(m^2+\frac{1}{m^2}-4\right)^2=36$
所以，
$$
\begin{aligned}
& m^2+\frac{1}{m^2}-4=6 \text{或者} m^2+\frac{1}{m^2}-4=-6 \\
& m^2+\frac{1}{m^2}=10 \text{或者} m^2+\frac{1}{m^2}=-2( \text{舍去}) \\
& \therefore\left(m-\frac{1}{m}\right)^2+2=10
\end{aligned}
$$
$$
\therefore\left(m-\frac{1}{m}\right)^2=8
$$
$$
\therefore\left(m-\frac{1}{m}\right)= \pm 2 \sqrt{2}
$$