Irrationality or Rationality of p1q given that pq=1 – math.stackexchange.com

Irrationality or Rationality of p1q given that pq=1 – math.stackexchange.com

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Let $p,q$ are irrational numbers such that $pq=1$. Then what can we say about character of $p+q$? i.e, $p+q$ is rational or irrational? Probably, I believe it is irrational but could not prove.

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