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#1 2011-08-19 21:36:44

engrymbiff
Member
Registered: 2010-06-14
Posts: 28

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

How to do this?

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#2 2011-08-19 22:20:36

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,648

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.

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#3 2012-10-12 23:28:25

engrymbiff
Member
Registered: 2010-06-14
Posts: 28

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

Sorry, that didn't help me..

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#4 2012-10-12 23:40:04

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,340
Website

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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#5 2012-10-12 23:48:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,648

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.

Online

#6 2012-10-13 02:22:40

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,836

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...


“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

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#7 2012-10-13 02:29:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,648

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.

Online

#8 2012-10-14 05:15:30

engrymbiff
Member
Registered: 2010-06-14
Posts: 28

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...

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#9 2012-10-14 23:55:57

scientia
Member
Registered: 2009-11-13
Posts: 222

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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