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Purge

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 · Posted: Sun Oct 21, 2007 9:37 pm *Post maybe stupid* 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.
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Purge · Posted: Sun Oct 21, 2007 10:12 pm *Post maybe stupid* 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 · Zone Hoster Joined: Feb 10 2004 Posts: 532 Offline

Consider this:

Life is like a box of chocolates, you never know what you're going to get.
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Cheese · Posted: Mon Oct 22, 2007 4:58 am *Post maybe stupid* Post subject:

good point.

i counter with this:
i like cookies.
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Bak · Posted: Mon Oct 22, 2007 1:45 pm *Post maybe stupid* 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?
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