Math Is Fun Forum

mp3qz

Member

Registered: 2009-07-21

Posts: 9

Inequality

1./    SOlve for min & max of:

[2./   img]http://latex.codecogs.com/gif.latex?x\neq&space;y\neq&space;z[/img]
Demonstrate

Last edited by mp3qz (2009-09-08 18:07:48)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Inequality

Hi mp3qz;

I think you also meant to say:

By the AM-GM

After much cancelling on the RHS.

Looking at each term we can see that they have a minimum when the numerator = 0 and that they are unbounded.
Undoing the substitutions:

Because each term is unbounded.

Last edited by bobbym (2009-09-10 04:33:25)

---

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.

mp3qz

Member

Registered: 2009-07-21

Posts: 9

Re: Inequality

but my teacher said : "=" has appear.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Inequality

Could you explain this bit more?

---

Why did the vector cross the road?
It wanted to be normal.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Inequality

H mathsyperson;

All three of the terms on the lhs have the same property. I chose this one for the explanation.

It is unbounded, intuitively meaning we can make it as large as we want. All three are like that. So if something is proven to be > 3 and it is unbounded it implies it is also >=5.

Last edited by bobbym (2009-09-10 05:01:32)

---

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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Inequality

Hi mp3qz;

It does appear in the >=.

---

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.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Inequality

Just because a term is unbounded (for each M there exists a choice of x, y, and z such that...) does not mean that it holds for every choice of x, y, and z.

---

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Inequality

Hi Ricky;

I am not asking it to hold for every choice of x,y, and z, what I am asking is that if it is already known to be greater than 3 and it is unbounded it also is greater than 5 , 11, 219, any number.

Last edited by bobbym (2009-09-10 09:31:47)

---

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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Inequality

Concerning proofs, you have to convince the other people that you are right. - Rene Thom

Two heads are better than one - Ghidrah

Since it is apparent that the last step:

Has not convinced either Ricky or mathsyperson, I am forced to withdraw it. I will retreat to this much:

Prove:

By the AM-GM

After some cancelling on the RHS.

Undoing the substitutions:

This is as far as I am sure of. Can anybody go any further towards answering the question?

Last edited by bobbym (2009-09-11 09:15:34)

---

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.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Inequality

Maybe it's significant that c = a+b?

---

Why did the vector cross the road?
It wanted to be normal.