RMO 2015!! #5

Algebra Level 5

If x,yx,y are non-zero numbers with x2+xy+y2=0x^2 + xy + y^2 = 0. Find :

(xx+y)2001+(yx+y)2001. \left( \frac{x}{ x+y } \right)^{2001} + \left( \frac{y}{x+y}\right) ^ { 2001}.

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