实数x,y满足x^3-y^3-3xy=1,则x-y=

实数x,y满足x^3-y^3-3xy=1,则x-y=
实数x,y满足x^3-y^3-3xy=1,则x-y=

实数x,y满足x^3-y^3-3xy=1,则x-y=
立方差公式
因为x^3-y^3=(x-y)(x^2+xy+y^2) x^3-y^3=1+3xy
所以1+3xy=(x-y)(x^2+xy+y^2)
x-y = (1+3xy)/(x^2+xy+y^2) =(1+3xy)/[(x-y)^2+3xy]
设x-y=A
则上式可化为:A=(1+3xy)/[A^2+3xy]
1+3xy=A3+A*3xy
所以 A=1