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

mn² = 15m²+ 17mn + 15n²

m²n = 20m² + 3n²

From equation 2, m^2 = 3*n^2/(n-20).

Set n=3*k^2 + 20 to simplify the calcs.

Then m=n/k. 

Drop this value in equation 1.  After a while a factor of n^2 drops out.  Substitue the value above for the remaining value of n and you get (k-5)(k^2 + 1) = 0 which is true only for k=5.

So m = 19 and n = 95.

 

 

 

Posted by xdog on 2007-04-27 10:59:26