\(\Delta=m^2-4\left(m-7\right)=\left(m-2\right)^2+24>0;\forall m\)
\(\Rightarrow\) Phương trình đã cho có 2 nghiệm pb với mọi m
Theo hệ thức Vi-ét: \(\left\{{}\begin{matrix}x_1+x_2=m\left(1\right)\\x_1x_2=m-7\left(3\right)\end{matrix}\right.\)
Khi đó: \(x_1=2x_2+12\)
\(\Leftrightarrow x_1-2x_2=12\left(2\right)\)
Từ (1), (2) ta có hệ: \(\left\{{}\begin{matrix}x_1+x_2=m\\x_1-2x_2=12\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x_1=m-x_2\\3x_2=m-12\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x_1=\dfrac{2m+12}{3}\\x_2=\dfrac{m-12}{3}\end{matrix}\right.\)(4)
Từ (3), (4)\(\Rightarrow\dfrac{2m+12}{3}\cdot\dfrac{m-12}{3}=m-7\)
\(\Leftrightarrow\left(2m+12\right)\left(m-12\right)=9\left(m-7\right)\)
\(\Leftrightarrow2m^2-12m-144=9m-63\)
\(\Leftrightarrow2m^2-21m-81=0\)
\(\Leftrightarrow\left[{}\begin{matrix}m=-3\\m=\dfrac{27}{2}\end{matrix}\right.\)
