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 December 23rd, 2017, 04:05 AM #1 Senior Member   Joined: Dec 2015 From: somewhere Posts: 514 Thanks: 80 Irrational numbers Find the two irrational numbers $\displaystyle (\alpha,\beta)$ such that $\displaystyle \alpha^2 - \beta \in N$
 December 23rd, 2017, 04:24 AM #2 Senior Member   Joined: Sep 2016 From: USA Posts: 609 Thanks: 378 Math Focus: Dynamical systems, analytic function theory, numerics $\alpha = \sqrt{\sqrt{2}+2}, \beta = 1 + \sqrt{2}$
 December 23rd, 2017, 04:24 AM #3 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,660 Thanks: 2635 Math Focus: Mainly analysis and algebra It's not "the two irrational numbers", there are an infinity of them. One suggestion: what if $\beta$ is a solution of, for example, $x^2-x-1=0$ (there are infinitely many other quadratics that would work).

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