Determine all possible quadruplets (A, B, P, Q) of positive integers, with P ≤ Q, that satisfy this system of equations:
A + B = 21, and:
A/P^{2} + B/Q^{2} = 1
Prove that these are the only quadruplets that exist.
(In reply to
re: Possible solution by Steve Herman)
Steve,
I'm afraid that's all the work I did on it (apart from some jottings on equalities of the form w/x^2+y/z^2=1) Once I got to the formula I gave, it seemed obvious that there could only be those answers, so I didn't explore further.

Posted by broll
on 20110118 01:57:24 