Find three positive rational numbers such that their sum is a square, and the sum of any pair exceeds the third by a square.

*Classical Rules: Let a "square" be any number that is the square of a rational number.*

(In reply to

re: Full solution by tomarken)

Only one word... OOPS!

But, though the example is "somewhat" (fully!) faulty, the formulas are good.

Let's try again: if x=4 and y=7, then (t+z)(t-z)=65, and t=9, z=4 is an answer, which produces a=65/2, b=16, c=65/2.