\(\Delta=9m^2+4m+4=\left(3m+\dfrac{2}{3}\right)^2+\dfrac{32}{9}>0;\forall m\)
Phương trình luôn có 2 nghiệm pb với mọi m
Theo Viet: \(\left\{{}\begin{matrix}x_1+x_2=-3m\\x_1x_2=-m-1\end{matrix}\right.\)
\(3\le x_1< x_2\Leftrightarrow\left\{{}\begin{matrix}\left(x_1-3\right)\left(x_2-3\right)\ge0\\\dfrac{x_1+x_2}{2}>3\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x_1x_2-3\left(x_1+x_2\right)+9\ge0\\x_1+x_2>6\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}-m-1+9m+9\ge0\\-3m>6\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}m\ge-1\\m< -2\end{matrix}\right.\) \(\Rightarrow\) Ko tồn tại m thỏa mãn
