已知x+y=-4，xy=-12，求y+1/x+1+x+1/y+1的值．

题目

已知x+y=-4，xy=-12，求

y+1

x+1

+

x+1

y+1

答案

原式=

(y+1)2+(x+1)2

(x+1)(y+1)

=

x2+y2+2(x+y)+2

xy+x+y+1

=

(x+y)2−2xy+2(x+y)+2

xy+x+y+1

∵x+y=-4，xy=-12，
∴原式=

16+24−8+2

−12−4+1

=−

34

15

．