Math Is Fun Forum

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 25,002

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Strange Ineq

a, b, c are positive.

a, b, c are real.

a*b*c = 1

Prove or find counterexamples:

a/b + b/c + c/a >= (a+b+c)/3

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'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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Strange Ineq

Hi;

There are no counterexamples.

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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.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 25,002

Website

Re: Strange Ineq

Are there any proofs?

---

'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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Strange Ineq

Yes, there are a number of them.

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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.

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,441

Website

Re: Strange Ineq

Video solution.

Last edited by zetafunc (2015-09-12 06:27:39)

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 25,002

Website

Re: Strange Ineq

Thanks.

Wasn't it a bit tough?

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'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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Strange Ineq

Search for the book: old_and_new_inequality.pdf

Problem 14 has solutions on p33.

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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.

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,441

Website

Re: Strange Ineq

Search for the book: old_and_new_inequality.pdf

Problem 14 has solutions on p33.

The problem there is posed with slightly different constraints on a, b, c, but the solutions look similar.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Strange Ineq

Hi;

If you have the proof for a + b + c then of course you have the proof for (a + b + c ) / 3

---

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.

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,441

Website

Re: Strange Ineq

Yes, but the problem in that PDF says that abc ≤ 1, whereas Agnishom's problem says that abc = 1.

However, it's true that this doesn't make any difference to the proof, apart from:

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Strange Ineq

Hi;

I agree.

---

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.