Determine all possible triplet(s) (p, q, r) of positive real numbers, with p ≤ q ≤ r, that satisfy the following system of equations:

p*q + q*r + p*r = 12 , and:
p*q*r = p + q + r + 2

(In reply to solution by Charlie)

Rereading the puzzle, I only now realize it asks for real numbers rather than integers only. But refining the search still appears to show that the 12 equality holds only at (2,2,2) for positive reals.

I realized this after Steve Herman found a non-integral negative solution.

Posted by Charlie on 2010-09-15 09:51:29