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Oct 21, 2017 at 17:07 history edited G Cab CC BY-SA 3.0
amended for irrational
Oct 21, 2017 at 16:24 comment added G Cab @nickgard: yes, you are right, I forgot that the only exception is when $a$ and $b$ are particular combinations of the same irrational number, in which case there is just one solution. Thanks for signalling, I will amend the answer.
Oct 21, 2017 at 15:51 comment added nickgard "Clearly, if $a$ or $b$ are irrational there are no solutions." I don't think this is correct. Example: I can draw a line from $(\sqrt{2},0)$ through $(1,1)$ to the $y$-axis at $(0,2+\sqrt{2})$. $$\frac{1}{\sqrt{2}}+\frac{1}{2+\sqrt{2}}=1$$
Oct 21, 2017 at 14:52 history edited G Cab CC BY-SA 3.0
edited central part
Oct 21, 2017 at 13:58 history answered G Cab CC BY-SA 3.0