*Problem:*

If are positive real numbers, such that , prove that

.

*Solution:*

From the AM-GM we deduce that

.

So,

.

Divide the last relation by . Then we get that

,

or

.

So, it is enough to prove that

.

But it holds that,

.

From this we need to prove now

.

That is,

,

which is obvious from the AM-GM inequality, *Q.E.D.*

Advertisements

it’s fine.i like it