MathDB
2011 PUMaC Individual Finals B2

Source:

September 24, 2019
algebra

Problem Statement

Prove for irrational number α\alpha and positive integer nn that (α+α2−1)1/n+(α−α2−1)1/n \left( \alpha + \sqrt{\alpha^2 - 1} \right)^{1/n} + \left(\alpha - \sqrt{\alpha^2 - 1} \right)^{1/n} is irrational.
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