\(A=x^2+2y^2+2xy-4x+6y+2020\)
\(A=\left(x^2+y^2+2^2+2xy-4y-4x\right)+\left(y^2+10y+25\right)+1991\)
\(A=\left(x+y-2\right)^2+\left(y+5\right)^2+1991\ge1991\)
Vậy \(Min_A=1991\)khi \(\hept{\begin{cases}x+y-2=0\\y+5=0\end{cases}}\hept{\begin{cases}x+y=2\\y=-5\end{cases}}\hept{\begin{cases}x=7\\y=-5\end{cases}}\)