Inequality

CatherineMorland · 2008-02-01 13:40:19

Identity · 2008-02-01 16:03:02

CatherineMorland wrote:

I'm going to use Lagrange multipliers (sorry, there's probably a much more elegant way)

Let

And Lagrange multipliers states that for some lambda,

So

And since

, the minimum is 3/2

Last edited by Identity (2008-02-01 16:17:00)

CatherineMorland · 2008-02-01 18:08:34

How do you know it is minimum and not maximum?

Identity · 2008-02-01 21:08:33

It can't have a maximum because as a, b, and c go to infinity, so does the entire expression. That's the only way I can tell

CatherineMorland · 2008-02-01 22:02:47

But

so they cant all go to infinity.

Identity · 2008-02-01 23:23:52

Oh dear, you're right, I don't really know what then

JaneFairfax · 2008-02-02 01:20:56

Hence the expression is not bounded above.

As for an alternative approach, how about starting with this:

Then just expand, rearrange, substitute for a+b+c and simplify.

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