Algebra or Geometry

Algebra Level 4

It is given that $2\cos \dfrac{2\pi}{n} = x+\dfrac{1}{x}$ for $n \in \mathbb N$ . If $x^{n} + \dfrac{1}{x^{n}} = an^{b}$ , where $a$ and $b$ are real numbers, find $a+b$ .