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Simultaneous Pythagorean Poser (Posted on 2015-07-04) Difficulty: 3 of 5
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

No Solution Yet Submitted by K Sengupta    
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solution | Comment 1 of 4
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

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