Letting s = x + y and p = xy we get the two equations
which in turn lead to
Jun 15th 2014, 04:10 PM
Re: Problem #9 - College Algebra
Thanks to all that helped out!
My solution is roughly the same as idea's and I have the unfortunate tendency to write out the first method I see, even if it isn't all that elegant. So here's my version in all it's multi-step glory!
And, as is well known:
So we have:
So subbing in from this and the the initial condition
With a little rearranging:
Letting z = xy
Since we are looking for integral solutions, let's try the rational root theorem. After sorting the list a bit to get all factors of 56 we find that z = -2 is the only rational solution. (The other two are irrational.) Now there is a detail we need to (quickly) look at. There is no a priori restriction here that says z must be an integer, only x and y. However if we look at the other two solutions for the z equation we can easily see that z = -2 is the only way to go.