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December 23rd, 2017, 05:05 AM   #1
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Irrational numbers

Find the two irrational numbers $\displaystyle (\alpha,\beta)$ such that $\displaystyle \alpha^2 - \beta \in N $
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December 23rd, 2017, 05:24 AM   #2
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$\alpha = \sqrt{\sqrt{2}+2}, \beta = 1 + \sqrt{2}$
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December 23rd, 2017, 05:24 AM   #3
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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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