已知X≠Y,X^3-X=5 ,Y^3-Y=5,求X^2+XY+Y^2的值.
參考答案:两式相减
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
已知X≠Y,X^3-X=5 ,Y^3-Y=5,求X^2+XY+Y^2的值.
參考答案:两式相减
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