Are there any non zero real triplet(s) (p, q, r) that satisfy the following system of equations?

p + 1/p = q, q + 1/q = r, and r + 1/r = p

If such triplet(s) exist, find at least one of these. Otherwise, prove that no such triplet can conform to the given conditions.

Agree completely with Charlie, but there is no need to do all those substitutions.

If p > 0, then so is q and r
But, p < q < r < p, which is impossible.

If p < 0, then so is q and r
But, p > q > r > p, which is impossible

And p cannot be 0

So, the equations have no real solution

Posted by Steve Herman on 2008-04-12 20:25:36