Question

已知x≠y,且x的三次方-x=7,y的三次方－y=7,那么x的平方+xy+y等于?

Answer 1

x^3-x=7
y^3-y=7
两式相减得
x^3-x-y^3+y=0
x^3-y^3-(x-y)=0
(x-y)(x^2+xy+y^2)-(x-y)=0
(x-y)(x^2+xy+y^2-1)=0
因为x≠y
所以x^2+xy+y^2-1=0
x^2+xy+y^2=1