已知x/y+y/x=2,求(x2+xy+y2)/(x2-4xy+y2)的值

问题描述:

已知x/y+y/x=2,求(x2+xy+y2)/(x2-4xy+y2)的值

x/y+y/x=2
(x2+y2)/xy=2
x2+y2=2xy
(x2+xy+y2)/(x2-4xy+y2)
=(2xy+xy)/(2xy-4xy)
=3xy/(-2xy)
=-3/2