Trash Talk - Continued Fractions Purge - Sun Oct 21, 2007 9:22 pm Post subject: Continued Fractions
Hi again.
I'm having trouble now with understanding the concept of continued fractions. Given the equation x^2 + x - 72 = 0 I have to prove that x = -9 or 8 using continued fractions.
I got up to the part by simplifying it to x = -1 + (72/x), but I can't figure out what to do from there.
Help is appreciated within 12 hours. Thanks. Dr Brain - Sun Oct 21, 2007 9:37 pm Post subject:
I've never used continued fractions (which probably means they're some kind of number theory thing), but I'd guess that you substitute -1 + 72/x for x in itself and expand. Recurse. Presumably this continued fraction converges on -9 and 8. I donno.
Purge - Sun Oct 21, 2007 10:12 pm Post subject:
Yeah, that's what you do, but I don't see how substituting -1 + 72/x into x infinitesmally will give you -9 or 8...
Confess - Mon Oct 22, 2007 1:33 am Post subject:
Consider this:
Life is like a box of chocolates, you never know what you're going to get.
Cheese - Mon Oct 22, 2007 4:58 am Post subject:
good point.
i counter with this:
i like cookies.
Bak - Mon Oct 22, 2007 1:45 pm Post subject:
x = -1 + 72/x
x = -1 + 72/(-1 + 72/x)
x = -1 + 72/(-1 + 72/(-1 + 72/x))
x = -1 + 72/(-1 + 72/(-1 + 72/(-1 + 72/x)))
...
i haven't taken number theory in a while, but don't infinite continued fractions represent irrational numbers and finite ones rational numbers?
