Algebra or Geometry

Algebra Level 4

It is given that 2cos2πn=x+1x 2\cos \dfrac{2\pi}{n} = x+\dfrac{1}{x} for nNn \in \mathbb N. If xn+1xn=anb x^{n} + \dfrac{1}{x^{n}} = an^{b} , where aa and bb are real numbers, find a+ba+b.

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