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It is given that 2cos2πn=x+1x 2\cos \dfrac{2\pi}{n} = x+\dfrac{1}{x}2cosn2π=x+x1 for n∈Nn \in \mathbb Nn∈N. If xn+1xn=anb x^{n} + \dfrac{1}{x^{n}} = an^{b} xn+xn1=anb, where aaa and bbb are real numbers, find a+ba+ba+b.
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