若非零复数x,y满足x²+xy+y²=0,则【x/(x+y)】^2005+【y/(x+y)】^2005的值是?

问题描述:

若非零复数x,y满足x²+xy+y²=0,则【x/(x+y)】^2005+【y/(x+y)】^2005的值是?
为了问答双方利益抄题目已校对,

x^2+xy+y^2=0,两边除以y^2得,(x/y)^2+x/y+1=0,根据求根公式得,x/y=(-1+√3i)/2,或x/y=(-1-√3i)/2,当x/y=(-1+√3i)/2时,x/(x+y)=1-y/(x+y)=1-1/(x/y+1)=(1+√3i)/2,y/(x+y)=(1-√3i)/2,当x/y=(...