ta có : \(x^2y+xy^2+x+y=2010\)(1)
\(\Leftrightarrow xy\times\left(x+y\right)+\left(x+y\right)=2010\)
\(\Leftrightarrow\)( xy + 1 ) ( x + y ) = 2010
mà xy=11 \(\Rightarrow\)xy+1=12
(1)\(\Leftrightarrow\)12 (x + y ) = 2010
\(\Leftrightarrow\)x + y = 167,5
lại có S\(=x^3+y^3\)
S \(=\left(x+y\right)^3-3xy\left(x+y\right)\)
S\(=167,5^3-3\times11\times167,5\)
S \(=\)4693894,375