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

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

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
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From: Bumpkinland
Registered: 2009-04-12
Posts: 96,619

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

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

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

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: Riemann Sphere
Registered: 2011-01-29
Posts: 21,748
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'
'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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#5 2012-10-12 23:48:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 96,619

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.

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

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

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

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

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 96,619

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.

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

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

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

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: 224

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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