Find all possible triplets (A, B, C) of positive integers, with A ≤ B, that satisfy this system of equations:

A² + B² = C², and:

A+B = C+12

Substitute C = (A+B) - 12 into the first equation.  The square terms conveniently cancel and the remaining terms can be factored as (A-12)*(B-12) = 72, giving solutions (A,B,C) = (84,13,85),  (48,14,50), (36,15,39), (30,16,34), (24,18,30), (21,20,29).

Edited on July 4, 2015, 11:54 am

Posted by xdog on 2015-07-04 11:53:12