\(\Delta=\left(2m-1\right)^2-4\left(m^2-1\right)=-4m+5>0\Rightarrow m< \frac{5}{4}\)
\(\left(x_1+x_2\right)^2-4x_1x_2=x_1+x_2-4x_2\)
\(\Leftrightarrow\left(2m-1\right)^2-4\left(m^2-1\right)=2m-1-4x_2\)
\(\Rightarrow4x_2=6m-6\Rightarrow x_2=\frac{3m-3}{2}\)
\(\Rightarrow x_1=2m-1-x_2=\frac{m+1}{2}\)
\(x_1x_2=m^2-1\Rightarrow\frac{3\left(m-1\right)\left(m+1\right)}{4}=m^2-1\)
\(\Leftrightarrow\frac{3}{4}\left(m^2-1\right)=m^2-1\)
\(\Leftrightarrow m^2-1=0\Rightarrow m=\pm1\)
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