Prove that for we have:

## July 17, 2011

## July 16, 2011

## July 14, 2011

## July 13, 2011

### Problem 236 (van khea)

Let . Prove that:

Proof

We have

Let then we have

We have

From Holder’s inequality we have

But we have

From AM-GM inequality we have

Therefore the proof is completed. Equality hold if

### Problem 234 (van khea)

Let . Prove that:

Proof

Let then we need to prove that:

We have

Because then from inequality we get:

From inequality we have

From inequality we have

Therefore the proof is completed. Equality holds for

## July 12, 2011

### Problem 232 (van khea)

Let be the lengths of the sides of a trangle such that . Prove that: