如果x2+xy=2,xy+y2=-1,则x2-y2=_,x2+2xy+y2=_.

问题描述:

如果x2+xy=2,xy+y2=-1,则x2-y2=______,x2+2xy+y2=______.

(1)∵x2-y2=x2+xy-xy-y2=x2+xy-(xy+y2
而x2+xy=2,xy+y2=-1,
∴x2-y2=2-(-1)=3;
(2)∵x2+2xy+y2=x2+xy+xy+y2
而x2+xy=2,xy+y2=1,
∴x2+2xy+y2
=x2+xy+xy+y2
=2-1
=1;
故答案为:3,1.