Refer to the earlier problem.

Can you find all possible non zero real quadruplet(s) (P, Q, R, S) that satisfy the following system of simultaneous equations?

2*Q = P + 19/P, and:

2*R = Q + 19/Q, and:

2*S = R + 19/R, and:

2*P = S + 19/S.

Bonus Question:

In the problem given above, if the number 19 was replaced throughout by a real constant M > 1, what would have been the possible non zero real quadruplet(s) (P, Q, R, S) that satisfy the given set of equations, in terms of M?

No idea why the problem is limited to M > 1.
The solution already given applies to all positive real values of M, for reasons already given.

Edited on May 29, 2008, 3:08 pm

Posted by Steve Herman on 2008-05-28 17:01:29