\(\Delta=m^2-8m+16=\left(m-4\right)^2\Rightarrow m\ne4\)
Theo Viet: \(\left\{{}\begin{matrix}x_1+x_2=m\\x_1x_2=2m-4\end{matrix}\right.\)
\(\left|x_1\right|+\left|x_2\right|=3\Leftrightarrow x_1^2+x_2^2+2\left|x_1x_2\right|=3\)
\(\Leftrightarrow\left(x_1+x_2\right)^2-2x_1x_2+2\left|x_1x_2\right|-9=0\)
\(\Leftrightarrow m^2-4m-1+4\left|m-2\right|=0\)
- Nếu \(m\ge2\) pt trở thành:
\(m^2-9=0\Rightarrow\left[{}\begin{matrix}m=3\\m=-3< 2\left(l\right)\end{matrix}\right.\)
- Nếu \(m< 2\) pt trở thành:
\(m^2-8m+7=0\Rightarrow\left[{}\begin{matrix}m=7>2\left(l\right)\\m=1\end{matrix}\right.\)
Vậy \(\left[{}\begin{matrix}m=1\\m=3\end{matrix}\right.\)
