If α and β are the roots of the equation x^2 - x + 1 = 0, then ^ 2009 + ^ 2009 =

JEE Main 2010 Mathematics question

If α and β are the roots of the equation , then

Answer: (2)

The roots are , with . Since 2009 = 6 × 334 + 5,

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Question ID VK-039261