\(\Delta=4m^2-12m+9+16m=4m^2+4m+9=\left(2m+1\right)^2+8>0\)
\(\Rightarrow\) pt luôn có 2 nghiệm pb
Theo Viet: \(\left\{{}\begin{matrix}x_1+x_2=2m-3\\x_1x_2=-4m\end{matrix}\right.\)
\(A=x_1^2+x_2^2=\left(x_1+x_2\right)^2-2x_1x_2\)
\(A=\left(2m-3\right)^2+8m\)
\(A=4m^2-4m+9=\left(2m-1\right)^2+8\ge8\)
\(\Rightarrow A_{min}=8\) khi \(2m-1=0\Rightarrow m=\frac{1}{2}\)