已知,x=1/2（√5+√3）y=1/2（√5-√3）.求x平方-xy+y平方和x/y+y/x的值

x²-xy+y²
=(x²-2xy+y²)+xy
=(x-y)²+xy
=[1/2(√5+√3)-1/2(√5-√3)]²+1/2(√5+√3)×1/2(√5-√3)
=(√3)²+1/4×(5-3)
=3+1/2
=7/2
x/y+y/x
=x²/(xy)+y²/(xy)
=(x²+y²)/(xy)
=[(x²+2xy+y²)-2xy]/(xy)
=[(x+y)²-2xy]/(xy)
=[(x+y)²/(xy)]-2
=﹛[1/2(√5+√3)+1/2(√5-√3)]²/[1/2(√5+√3)×1/2(√5-√3)]﹜-2
=(√5)²/[1/4×(5-3)]-2
=[5/(1/2)]-2
=10-2
=8 再答： 不客气，有帮助采纳下吧
再问： 为什么要-2呢
再答： 化简了吗-2xy/(xy)就变成-2了
再问： 哦，知道了，谢谢