Let α and β be the roots of x^2 - 6x - 2 = 0, with > . If a_n = ^n - ^n for n 1, then the value of a_ 10 - 2a_8 2a_9 is

JEE Advanced 2011 Mathematics question

Let α and β be the roots of , with . If for , then the value of is

Answer: (C)

α and β satisfy , so and . Subtracting:

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Question ID VK-025926