已知实数x、y满足x+y+xy=9,x2y+xy2=20,求x2+y2的值.

x+y+xy=9
x+y=9-xy
x^2y+xy^2=20
xy(x+y)=20
xy(9-xy)=20
xy^2-9xy+20=0
(xy-4)(xy-5)=0
xy=4或xy=5
x+y=5或x+y=4
x^2+y^2
=(x+y)^2-2xy
=4^2-2*5
=6
或
x^2+y^2
=(x+y)^2-2xy
=5^2-2*4
=17
所以x^2+y^2的值为6或17