Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

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**engrymbiff****Member**- Registered: 2010-06-14
- Posts: 30

How to do this?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,590

Hi;

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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**engrymbiff****Member**- Registered: 2010-06-14
- Posts: 30

Sorry, that didn't help me..

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Hi Bobbym,

Is it okay to start with the thing we are trying to prove?

'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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,590

Hi;

This is the problem:

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 15,937

Hi bobbym

I think what Agnishom wanted to ask you is whether it is okay to start the proof with what we want to prove and work our way to a true statement...

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,590

Hi anonimnystefy;

I missed that. I am sorry about that. Bob and I had a good discussion on that and it seems better to work backwards in that case. Even though they do work forwards a lot in inequality books.

Unfortunately, whatever brilliant idea I had about this problem 1 year ago, I can not remember it at all.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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**engrymbiff****Member**- Registered: 2010-06-14
- Posts: 30

Hm... I really cannot solve it, I have a vague memory of how I solved it last time but now I don't have a good clue of how...

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**scientia****Member**- Registered: 2009-11-13
- Posts: 224

I have a very weird solution; you probably won't like it but I'll have a go anyway.

Let .

Then

because .Let

.We find

(just). It follows that since the quadratic function is strictly increasing for positiveThe LHS is

and so we are done.Offline

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