\(\Delta'=\left(m-1\right)^2-\left(m+1\right)\left(m-3\right)=4>0\)
Phương trình luôn có 2 nghiệm pb \(\forall m\ne1\)
Mặt khác ta có \(\left|x_1-x_2\right|=\left|\frac{2\sqrt{\Delta'}}{a}\right|=\left|\frac{4}{m+1}\right|\)
\(\left|x_1^2-x_2^2\right|=4\Leftrightarrow\left|\left(x_1-x_2\right)\left(x_1+x_2\right)\right|=4\)
\(\Leftrightarrow\left|\frac{8\left(m-1\right)}{\left(m+1\right)^2}\right|=4\) \(\Leftrightarrow2\left|m-1\right|=\left(m+1\right)^2\)
\(\Leftrightarrow m^2+2m+1-2\left|m-1\right|=0\)
- Nếu \(m>1\Rightarrow m^2+2m+1-2m+2=0\)
\(\Leftrightarrow m^2=-3\) (vô nghiệm)
- Nếu \(m\le1\Leftrightarrow m^2+2m+1-2+2m=0\)
\(\Leftrightarrow m^2+4m-1=0\Rightarrow m=-2\pm\sqrt{5}\)
