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#1 2011-08-20 19:36:44

engrymbiff
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Show that (413)^(1/3)>6+3^(1/3)

How to do this?

#2 2011-08-20 20:20:36

bobbym
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Re: Show that (413)^(1/3)>6+3^(1/3)

Hi;


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#3 2012-10-13 22:28:25

engrymbiff
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Re: Show that (413)^(1/3)>6+3^(1/3)

Sorry, that didn't help me..

#4 2012-10-13 22:40:04

Agnishom
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Re: Show that (413)^(1/3)>6+3^(1/3)

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'
'Who are you to judge everything?' -Alokananda

#5 2012-10-13 22:48:13

bobbym
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Re: Show that (413)^(1/3)>6+3^(1/3)

Hi;

This is the problem:


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#6 2012-10-14 01:22:40

anonimnystefy
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Re: Show that (413)^(1/3)>6+3^(1/3)

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...


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#7 2012-10-14 01:29:10

bobbym
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Re: Show that (413)^(1/3)>6+3^(1/3)

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#8 2012-10-15 04:15:30

engrymbiff
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Re: Show that (413)^(1/3)>6+3^(1/3)

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...

#9 2012-10-15 22:55:57

scientia
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Re: Show that (413)^(1/3)>6+3^(1/3)

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 positive x.







The LHS is
and so we are done.

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