- #1

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## Homework Statement

If ##a+\frac{1}{a}=\sqrt{3}##, then ##a^{2016} + (\frac{1}{a})^{2016} ## equals

A. 0

B. 1

C. √2

D. √3

E. 2

## Homework Equations

## The Attempt at a Solution

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I find no real solution for a.

What I can do is just find a^2 + (1/a)^2 which equals 1, a^4 + (1/a)^4 = -1, a^8 + (1/a)^8 = -1, and so on...

Since 2016 is not a square number, I don't know how to determine the value

Is there any theory about problem like this?

Please help