\(\Delta=m^2-4\left(m-6\right)=m^2-4m+24=\left(m-2\right)^2+20>0\)
=> PT có hai nghiệm với mọi m
theo VE
\(\left\{{}\begin{matrix}x_1+x_2=m\\x_1x_2=m-6\end{matrix}\right.\)
\(\left|x_1-x_2\right|=2\sqrt{5}\Leftrightarrow\sqrt{\left(x_1+x_2\right)-4x_1x_2}=2\sqrt{5}\)
\(\Leftrightarrow m^2-4\left(m-6\right)=20\Leftrightarrow m^2-4m+4=0\)
\(\Leftrightarrow\left(m-2\right)^2=0\Leftrightarrow m=2\)