\(x^2y+xy^2+x+y=2016\Leftrightarrow\left(x+y\right)\left(xy+1\right)=2016\)
\(\Leftrightarrow42\left(x+y\right)=2016\Leftrightarrow x+y=48\)
\(\Leftrightarrow\left(x+y\right)^2=2304\Leftrightarrow x^2+y^2+2xy=2304\)
Do đó: \(A=x^2+y^2-5xy=x^2+y^2+2xy-7xy=2304-7.41=2017\)