Find x^{2}+y^{2} if x and y are positive integers such that

x y+x+y=71 \quad \text { and } \quad x^{2} y+x y^{2}=880

Find x^{2}+y^{2} if x and y are positive integers such that

x y+x+y=71 \quad \text { and } \quad x^{2} y+x y^{2}=880