实数x,y满足x的三次方-y的三次方-3xy=1则x-y=

2024-11-18 00:50:06
推荐回答(1个)
回答1:

首明握先x3-y3=(x-y)(x2+xy+y2) 其次 x3-y3-3xy=1
所以 x3-y3=1+3xy=(x-y)(x2+xy+y2)

x-y = (1+3xy)/歼槐(x2+xy+y2) =(1+3xy)/[(x-y)2+3xy]

设x-y=A

则上式可化为氏槐友 A=(1+3xy)/[A2+3xy]
1+3xy=A3+A*3xy
所以 A=1