Question

设（x-1)(y+1)=3,且xy(x-y)=4.求x²+y²

Answer 1

(x-1)(y+1)=3
xy+(x-y)=4
xy(x-y)=4
xy=2
x-y=2

x²+y²=(x-y)²+2xy
=4+4
=8

Answer 2

解
设（x-1)(y+1)=3, xy+x-y-1=4, xy+(x-y)=5
且xy(x-y)=4.
解得xy=1,x-y=4
或 x-y=1 xy=4

求x²+y²=(x-y)²+2xy=16+2=18

x²+y²=(x-y)²+2xy=1+8=9

对你有启发，祝你学习进步。