\(\Delta'=\left(m-1\right)^2+m^2>0\) \(\forall m\) phương trình luôn có 2 nghiệm pb
Theo Viet: \(\left\{{}\begin{matrix}x_1+x_2=-2\left(m-1\right)\\x_1x_2=-m^2\end{matrix}\right.\)
\(\left|x_1\right|-\left|x_2\right|=6\Rightarrow\left(\left|x_1\right|-\left|x_2\right|\right)^2=36\)
\(\Rightarrow x_1^2+x_2^2-2\left|x_1x_2\right|=36\)
\(\Rightarrow\left(x_1+x_2\right)^2-2x_1x_2-2\left|x_1x_2\right|=36\)
\(\Rightarrow4\left(m-1\right)^2+2m^2-2\left|-m^2\right|=36\)
\(\Rightarrow4m^2-8m+4+2m^2-2m^2-36=0\) (\(m^2\ge0\Rightarrow\left|-m^2\right|=m^2\))
\(\Rightarrow4m^2-8m-32=0\Rightarrow\left[{}\begin{matrix}m=4\\m=-2\end{matrix}\right.\)
