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RMO 2015!! #5

Algebra Level 5

If \(x,y\) are non-zero numbers with \(x^2 + xy + y^2 = 0\). Find :

\[ \left( \frac{x}{ x+y } \right)^{2001} + \left( \frac{y}{x+y}\right) ^ { 2001}. \]

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by Dev Sharma

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