1.\(m=-2\)
\(\Leftrightarrow x^2-2\left(-2+1\right)x+-2-4=0\)
\(\Leftrightarrow x^2+2x-6=0\)
\(\Delta=2^2-4.-6=4+24=28>0\)
\(\rightarrow\left\{{}\begin{matrix}x_1=\dfrac{-2-2\sqrt{7}}{2}=-1-\sqrt{7}\\x_2=\dfrac{-2+2\sqrt{7}}{2}=-1+\sqrt{7}\end{matrix}\right.\)
2.\(\Delta=\left(2\left(m+1\right)\right)^2-4\left(m-4\right)\)
\(=4\left(m+1\right)^2-4\left(m-4\right)=4\left(m^2+2m+1\right)-4\left(m-4\right)\)
\(=4m^2+8m+4-4m+16=4m^2+4m+20\)
\(=\left(2m+1\right)^2+19\ge19>0\)
=> pt luôn có 2 nghiệm phân biệt với mọi m
3.Theo hệ thức Vi-ét, ta có:\(\left\{{}\begin{matrix}x_1+x_2=2m+2\\x_1.x_2=m-4\end{matrix}\right.\)
\(A=x_1\left(1-x_2\right)+x_2\left(1-x_1\right)\)
\(=x_1-x_1x_2+x_2-x_1x_2=x_1+x_2-2x_1x_2\)
\(=-2m-2-2\left(m-4\right)=2m+2-2m+8=10\)
=> A không phụ thuộc vào m
