已知实数x,y满足（x+y)平方=1,(x-y)平方=25,则x平方-y平方+xy=( )

(x+y)^2=1
x+y=1或x+y=-1
(x-y)^2=25
x-y=5 或x-y=-5
x=3,y=-2,或x=-2,y=3,或x=2,y=-3,或x=-3,y=-2
x^2-y^2=5或-5
(1)-(2)
4xy=-24
xy=-6
x^2-y^2+xy=5-6=-1或=-5-6=-11

因（x+y)^2=1,(x-y)^2=25,故两式相乘开方得：|x^2-y^2|=5===>x^2-y^2=5或-5..两式展开相减得：xy=-6.故x^2-y^2+xy=-1,或-11.