since
So we want
Since 5 is coprime to 11 it must be that
Now, since 11 is prime, it follows that it divides the product if and only if it divides one of the 2 factors.
So the solutions are: and
So our class was given this to look over before our last class before the break:
I got a value that works,
but not sure if this is the only answer and I went about it probably not in the correct fashion.
What I did was just notice that , then I though that if , then , and it turns out that as well.
I doubt you can just eliminate terms like this to make it work.
All the examples I've read here don't deal with anything more than say or whatever. So I wasn't sure how to approach when a whole quadratic equation was on the LHS.
Also, the quadratic formula doesn't give any real solutions, so my original theory of using that doesn't work.
Any help would be appreciated, Thanks.