Deep root

Algebra Level 5

The real solution of the equation below can be expressed as x=z+zx=z+z^{*}, where zz is a complex number, with z=1|z|=1. If argz=abπ\arg{z}=\frac{a}{b}\pi, where aa and bb are co-prime, find bab-a. x=2+22+xx=\sqrt{2+\sqrt{2-\sqrt{2+x}}}

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