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Simultaneous Pythagorean Poser (
Posted on 20150704
)
Find all possible triplets (A, B, C) of
positive integers
, with A ≤ B, that satisfy this system of equations:
A
^{2}
+ B
^{2}
= C
^{2}
, 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 (A12)*(B12) = 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 20150704 11:53:12
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