\(A=x^2+2y^2+2xy+2x-4y+2032\)
\(=\left(x^2+y^2+1+2xy+2x+2y\right)+\left(y^2-6x+9\right)+2022\)
\(=\left(x+y+1\right)^2+\left(y-3\right)^2+2022\ge2022\)
\(A_{min}=2022\) khi \(\left(x;y\right)=\left(-4;3\right)\)
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