Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**rimi****Member**- Registered: 2006-02-21
- Posts: 17

prove that ,

u (to the power)n × v(to the power)(1-n) ≤nu + (1-n)v

n∈(o,1) and u,v > 0

by the way how do I bring this superscripts ? As word files are not working.

Offline

**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,552

To do superscripts:

`u[sup]n[/sup]`

and you get:

u[sup]n[/sup]

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,850

Hence, the question would be.....

Prove that u[sup]n[/sup] x v[sup]1-n[/sup]≤nu+(1-n)v

where

n∈(o,1) and u,v > 0

Character is who you are when no one is looking.

**Online**

**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

If n = 0, then the inequality simplifies down to v ≤ v.

Similarly, if n = 1, then the inequality simplifies down to u ≤ u.

So u[sup]n[/sup] x v[sup]1-n[/sup] ≤ nu+(1-n)v all the time because they are actually always equal to each other.

Why did the vector cross the road?

It wanted to be normal.

Offline

**rimi****Member**- Registered: 2006-02-21
- Posts: 17

No mathsy thats not quite a proof...but I can give you hints if you want...this is simple...indeed

Offline

**rimi****Member**- Registered: 2006-02-21
- Posts: 17

I guess I can give you some hints about the solution...you can consider the fact that log is a concave function.

Offline

**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

We must prove that

log(nu+(1-n)v)>=nlog(u)+(1-n)log(v)

Is there some unequation for

log(a+b) and log(a)+log(b)?

IPBLE: Increasing Performance By Lowering Expectations.

Offline

**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

Rimiq please, help us more.

IPBLE: Increasing Performance By Lowering Expectations.

Offline

Pages: **1**