Find all real pairs (p, q) satisfying the following system of equations:
���� ���� ����� ����� p - 1/p - q² = 0

���� ���� ����� ����� q/p + pq = 4

(In reply to Analytical solution by Federico Kereki)

you say:

Multiplying both results, 4=(16-q^6)/q^2, so q^6-4q^2-16=0. Writing q^2=r we get r^3-4r-16=0 which has a single real root r=2, so if q=��2 then p=1+��2, and if q=-��2, then p=1-��2.

correction:

Multiplying both results, 4=(16-q^6)/q^2, so q^6-4q^2-16=0. Writing q^2=r we get    r^3+4r-16=0         which has a single real root r=2, so if q=��2 then p=1+��2, and if q=-��2, then p=1-��2.

Posted by Ady TZIDON on 2007-07-11 07:19:10