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We want to calculate the value of x if x were this continued fraction:

On our way, we will see how quadratic equations are involved.

*Last edited by Agnishom (2014-10-26 23:50:11)*

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,118

Responding To Thread As Being Told.

I wish I was in Dixie, Hooray! Hooray!...

"Non tutte le ciambelle riescono col buco.”

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What is amazing is that the whole fraction in the large box and the part inside the smaller box is just the exact same since both constitute the same iterations infinite times.

Do you agree?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,118

I don't understand.

I wish I was in Dixie, Hooray! Hooray!...

"Non tutte le ciambelle riescono col buco.”

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Do you think that the whole continued fraction and the part inside the smaller box is just the same?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,118

Yes

I wish I was in Dixie, Hooray! Hooray!...

"Non tutte le ciambelle riescono col buco.”

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Great!

On the basis of that, we can write it as this:

Can we?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,118

Yes

I wish I was in Dixie, Hooray! Hooray!...

"Non tutte le ciambelle riescono col buco.”

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Do you know how to solve this?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,118

x^2 = 1 + x

I wish I was in Dixie, Hooray! Hooray!...

"Non tutte le ciambelle riescono col buco.”

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Great!

Use the quadratic formula from there onwards

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,118

For?

Lets learn more.

*Last edited by David (2014-10-27 00:40:32)*

I wish I was in Dixie, Hooray! Hooray!...

"Non tutte le ciambelle riescono col buco.”

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Do we know what the quadratic formula is?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,118

Explain

I wish I was in Dixie, Hooray! Hooray!...

"Non tutte le ciambelle riescono col buco.”

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It is a shorthand formula that can solve *any* quadratic equation just by plugging values without the need of any intelligent thought!

*Last edited by Agnishom (2014-10-27 01:17:34)*

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,118

ax^2 + bx + c = 0

I wish I was in Dixie, Hooray! Hooray!...

"Non tutte le ciambelle riescono col buco.”

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Okay let me write down the formula here!

What is the value of a,b and c in this equation: x^2 +5x+6 =0?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,118

I haven't learnt that.

I wish I was in Dixie, Hooray! Hooray!...

"Non tutte le ciambelle riescono col buco.”

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You will now.

Do you agree that every quadratic equation is reducable to the form in post 16?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,118

I don't think so?

I wish I was in Dixie, Hooray! Hooray!...

"Non tutte le ciambelle riescono col buco.”

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Well, it is.

Is x^2+5x+6 of that form?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,118

Yes.

I wish I was in Dixie, Hooray! Hooray!...

"Non tutte le ciambelle riescono col buco.”

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What are the values of a, b, and c?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,118

a = ^2 b = 5 c = 6

I wish I was in Dixie, Hooray! Hooray!...

"Non tutte le ciambelle riescono col buco.”

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No, a=1. Do you agree?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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