Question

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

Answer 1

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