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Homework Statement
The difference between cubes of two natural numbers is 208. Which are those two numbers?
Homework Equations

The Attempt at a Solution
Here is how I set it up.
x[tex]\widehat{}^{}3[/tex]  (xy)[tex]\hat{}3 = 208[/tex], which leads to ...
x[tex]\hat{}2(3y)[/tex] + x(3y[tex]\hat{}2)[/tex] + (y[tex]\hat{}3  208)[/tex] = 0
I figured, since this is now a quadratic equation and I'm looking for a solution where the curve only touches the xaxis, D = b^2  4ac would have to be zero. But when I put that in, it just doesn't budge. I know y = 4 and x = 6, but for the love of God, I can't get to that solution. I'm really starting to get nervous, since this is supposed to be an easy problem, but I just can't see what I'm doing wrong to not get to the solution.
Any help would be greatly appreciated.
edit: After charting it out, I see that the determinant isn't zero, so I got that wrong, but I still don't see what I need to do to get y = 4.
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