Positive rationals satisfying: $a^2+a^2=c^2$?

Question

If there are none why not?

Thanks in advance.

Nigh-trivially, if there were then the square root of two would be rational ($a^2+a^2=c^2$, so $2a^2=c^2$, so $2=\frac{c^2}{a^2}$). — Steven Stadnicki, Jul 19 '13 at 21:58

score 6 · Accepted Answer · answered Jul 19 '13 at 21:58

6

Note that this can be written as $$2=\left(\frac{c}a\right)^2$$

Is $\sqrt 2$ rational?

answered Jul 19 '13 at 21:58

Pedro

1 Answers1