Hello, I can't seem to understand how to use continued fractions to find the value of x in: x^2 + x - 72 = 0

Can someone please explain how to solve this problem? Basically, I need to prove that x = -9 or 8.

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- Oct 21st 2007, 03:22 PMvpereraContinued Fractions
Hello, I can't seem to understand how to use continued fractions to find the value of x in: x^2 + x - 72 = 0

Can someone please explain how to solve this problem? Basically, I need to prove that x = -9 or 8. - Oct 21st 2007, 04:08 PMgalactus
Try this.

Now, perform the iterations.

Hopefully, it convegres to the solutions. It may not do it too fast, though. - Oct 21st 2007, 04:19 PMvperera
Actually, I'm totally new to the continued fractions thing. Could you explain what these iterations are?

- Oct 21st 2007, 04:22 PMgalactus
See what x equals?. See the x under the 72?. Keep subbing it in, ad infinitum.

Do it enough and it should converge to the solution(s) - Oct 21st 2007, 04:33 PMvperera
Keep subbing what into x?

- Oct 21st 2007, 04:44 PMvperera
Oh, so sub -1 + 72/x into x, right?

And what do you mean keep subbing to infinity? - Oct 21st 2007, 05:37 PMThePerfectHacker
- Oct 21st 2007, 06:08 PMvperera
can you explain that to me in lay man's terms? :)

- Oct 21st 2007, 06:17 PMThePerfectHacker
(I made a pathetic mistake instead of it should be for ).

Consider the positive solution is .

Now it means

You form the continued fraction or simply 1's so .

Now let represent the fraction (approximation) after the terms.

So and the difference between the real value is .

Now and the difference between the real value is .

This tells us the difference between the approximation and the actual value gets very close. - Oct 21st 2007, 07:13 PMvperera
I still don't understand.. could you use my problem as an example? x^2 +x - 72 = 0