7.
\(\Delta'=9-\left(m+4\right)=5-m\)
Pt có 2 nghiệm khi: \(5-m\ge0\Rightarrow m\le5\)
Theo hệ thức Viet: \(\left\{{}\begin{matrix}x_1+x_2=6\\x_1x_2=m+4\end{matrix}\right.\)
\(2020\left(x_1+x_2\right)-2021x_1x_2=2014\)
\(\Leftrightarrow2020.6-2021\left(m+4\right)=2014\)
\(\Leftrightarrow m=\dfrac{2022}{2021}\) (thỏa mãn)
8.
\(\Delta'=m^2+1>0;\forall m\Rightarrow pt\) luôn có 2 nghiệm pb với mọi m
Theo hệ thức Viet: \(\left\{{}\begin{matrix}x_1+x_2=2m\\x_1x_2=-1\end{matrix}\right.\)
\(x_1^2+x_2^2-x_1x_2=7\)
\(\Leftrightarrow\left(x_1+x_2\right)^2-3x_1x_2=7\)
\(\Leftrightarrow4m^2+3=7\)
\(\Leftrightarrow m^2=1\)
\(\Rightarrow m=\pm1\)
