非零复数X,Y满足X2 XY Y2=0,则(X／X Y)的2005次方 (Y／X Y)的2005次方的值是多少

我急着要答案

热心网友

应该是X2+ XY+ Y2=0,则(X／X+ Y)的2005次方+ (Y／X +Y)的2005次吧!由x^2+xy+y^2=0得(x+y)^2=xy,故有(x+y)^2004=(xy)^1002及(x-y)(x^2+xy+y^2)=0,所以有x^3=y^3所以［x/(x+y)^］2005+［y/(x+y)^］2005 =(x^2005+y^2005)/(x+y)^2005 =［(x^3)^668*x+(y^3)^668*y］/(x+y)^2005 =(x^3)^668/(x+y)^2004 =(x^3)^668/(xy)^1002 =(x^3)^668/(x^3)^334*(y^3)^334 =(x^3)^668/(x^3)^668 =1