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

                      q/p + pq = 4

p-1/p=q²
q(p+1/p)=4
square the second eq, q²*(p+1/p)²=16
(p-1/p)*((p-1/p)²+4)=16
let p-1/p=x 
x³+4x-16=0 => (x-2)*(x²+2x+8)=0
x²+2x+8=0 has no real roots as its discriminant is less than 0
x=2 is the only solution.
Solving p-1/p=2 yields p=(1(+/-)√2)
substitute these in eq(2) to get q=+√2 for p=(1+√2)
and q=-√2 for p=(1-√2)

Edited on July 10, 2007, 11:48 am

Posted by Praneeth Yalavarthi on 2007-07-10 11:44:22