\(\Delta'=m^2-m^2+2=2>0\Rightarrow\) pt luôn có 2 nghiệm pb
Theo Viet: \(\left\{{}\begin{matrix}x_1+x_2=2m\\x_1x_2=m^2-2\end{matrix}\right.\)
\(\left|x_1^3-x_2^3\right|=10\sqrt{2}\Leftrightarrow\left(x_1^3-x_2^3\right)^2=200\)
\(\Leftrightarrow\left(x_1-x_2\right)^2\left[\left(x_1+x_2\right)^2-x_1x_2\right]^2=200\)
\(\Leftrightarrow\left[\left(x_1+x_2\right)^2-4x_1x_2\right]\left[\left(x_1+x_2\right)^2-x_1x_2\right]^2=200\)
\(\Leftrightarrow\left(4m^2-4m^2+8\right)\left(4m^2-m^2+2\right)^2=200\)
\(\Leftrightarrow\left(3m^2+2\right)^2=25\Rightarrow\left[{}\begin{matrix}3m^2+2=5\\3m^2+2=-5\left(vn\right)\end{matrix}\right.\)
\(\Rightarrow3m^2=3\Rightarrow m=\pm1\)
