Prove that $Ae+B/e$ is irrational.

pokoljitef2
2022-06-27
Answered

Prove that $Ae+B/e$ is irrational.

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candelo6a

Answered 2022-06-28
Author has **24** answers

Suppose that $Ae+B/e$ is rational. Then $Ae+B/e=p/q$ for some $p,q\in \mathbb{Z}$. Then $A{e}^{2}-\frac{p}{q}e+B=0$. Clearing denominators gives us e as a root of $Aq{x}^{2}-px+Bq$ which is impossible since $e$ is transcendental.

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