设x=2+根号3/2-根号3,y=2-根号3/2+根号3,求x的3次方+y的3次方的值

设x=2+根号3/2-根号3,y=2-根号3/2+根号3,求x的3次方+y的3次方的值
设x=2+根号3/2-根号3,y=2-根号3/2+根号3,求x的3次方+y的3次方的值

设x=2+根号3/2-根号3,y=2-根号3/2+根号3,求x的3次方+y的3次方的值
x=(2+√3)/(2-√3)
x=(2+√3)^2/(2-√3)(2+√3)
x=(2+√3)^2
x=7+4√3
y=(2-√3)/(2+√3)
y=(2-√3)^2/(2-√3)(2+√3)
y=(2-√3)^2
y=7-4√3
x^3+y^3
=(x+y)(x^2-xy+y^2)
=(x+y)[(x^2+2xy+y^2)-3xy]
=(x+y)[(x+y)^2-3xy]
=(7+4√3+7-4√3)[(7+4√3+7-4√3)^2-3(7-4√3)(7-4√3)]
=14*[14^2-3*(49-48)]
=14*[14^2-3]
=2702