Determine all possible real pairs (m,n) satisfying the following system of equations:

mn² = 15m²+ 17mn + 15n²

m²n = 20m² + 3n²

From initial observation, it becomes apparent that n > 20, from the second equation:

m²(20-n) + 3n² = 0

m² = 3n²/(n-20)

m = ±n√[3/(n-20)]

Substituting this into the first equation yields for the positive root:

m=19, n=95

For the negative root, the function increases from 20 → ∞.  Therefore, this root does not satisfy the equation for real solutions.  Thus the only solution is:

m=19, n=95

Posted by hoodat on 2007-04-27 18:08:36