\(\Delta'=1-4\left(2m-4\right)=17-8m\ge0\Rightarrow m\le\frac{17}{8}\)
Theo Viet ta có: \(\left\{{}\begin{matrix}x_1+x_2=-1\\x_1x_2=2m-4\end{matrix}\right.\)
Mặt khác do \(x_1\) là nghiệm nên \(x_1^2+x_1+2m-4=0\Rightarrow x_1^2=-x_1-2m+4\)
\(\Rightarrow x_1^2=2x_2+5\)
\(\Leftrightarrow-x_1-2m+4=2x_2+5\)
\(\Leftrightarrow x_1+2x_2=-2m-1\)
Kết hợp Viet ta có hệ: \(\left\{{}\begin{matrix}x_1+x_2=1\\x_1+2x_2=-2m-1\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x_1=2m+3\\x_2=-2m-2\end{matrix}\right.\)
Mà \(x_1x_2=2m-4\Leftrightarrow\left(2m+3\right)\left(-2m-2\right)=2m-4\)
\(\Leftrightarrow\left(2m+3\right)\left(m+1\right)=-m+2\)
\(\Leftrightarrow2m^2+6m+1=0\) \(\Rightarrow m=\frac{-3\pm\sqrt{7}}{2}\)
