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

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

How to do this?

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

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### 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.
Always satisfy the Prime Directive of getting the right answer above all else.

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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: 24,835
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'
I'm not crazy, my mother had me tested.

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

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### 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.
Always satisfy the Prime Directive of getting the right answer above all else.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### 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
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### 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.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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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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