MathJax(?): Can't find handler for document MathJax(?): Can't find handler for document I suggested the following problem to my friend: prove that there exist irrational numbers a and b such that ab is rational.Now, his inital solution was like this: let&#39;s take a rational number r and an irrational number i. Let&#39;s assume a = r i

Question

MathJax(?): Can&#039;t find handler for document MathJax(?): Can&#039;t find handler for document I suggested the following problem to my friend: prove that there exist irrational numbers a and b such that ab is rational.Now, his inital solution was like this: let&amp;#39;s take a rational number r and an irrational number i. Let&amp;#39;s assume   a  =      r    i

soosenhc · Accepted Answer

Consider       2                  log        2            ⁡      3

babyagelesszj · Accepted Answer

Let   r be a positive rational number and i a positive irrational number. If       r          i       is rational, then       r    i    =      a    b   for a,  a  ,  b  ∈      Z   such that  b  ≠  0. In particular,   i  =      log          r        ⁡      (          a      b        )  .