By symmetry all solutions must have p=q. So the equation simplifies to
2p + 2/p + 4 = 4*sqrt(2p+1)
And then to the polynomial
16p^4 + 8p^3 + 8p^2 + 4p + 1 = 0
Which has no real roots.
If I have made no errors the equation has no real solutions.
Edit: I did make an error. The polynomial should be
p^4  4p^3 + 2p^2 + 4p + 1 = 0
as xdog pointed out the roots are p=1±√2
but the one with the minus is extraneous that arises from squaring both sides.
The only real solution is p=1+√2
Edited on May 12, 2015, 9:01 am

Posted by Jer
on 20150511 10:15:26 