Posted by Anonymous on Monday, January 23, 2012 at 8:30pm.
4x^2 + kxy - 9y^2
k = (4x^2 + 9y^2)/xy
let x = 3m and y = 2m
k = (36m^2 + 36n^2)/6mn
k = 6m/n + 6n/m
So, we see that n must divide 6m and m must divide 6n
If m=1, n divides 6: 1,2,3,6
If m=2, n divides 12: 1,2,3,4,6,12
and so on
Now, how many of those values of m and m determine unique values for k, I don't know. Have fun!
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