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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: 3,123

Responding To Thread As Being Told.

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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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: 3,123

I don't understand.

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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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: 3,123

Yes

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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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: 3,123

Yes

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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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: 3,123

x^2 = 1 + x

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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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: 3,123

For?

Lets learn more.

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

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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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: 3,123

Explain

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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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: 3,123

ax^2 + bx + c = 0

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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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: 3,123

I haven't learnt that.

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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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: 3,123

I don't think so?

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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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: 3,123

Yes.

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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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: 3,123

a = ^2 b = 5 c = 6

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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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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