*Problem:*

If for are positive real numbers then prove that

*Solution(An Idea by Vo Quoc Ba Can):*

We only need to prove that

for all .

So, using the AM-GM Inequality we have that

.

It follows that

.

Therefore it suffices to prove that

,

which is obviously true from the AM-GM Inequality, *Q.E.D.*

### Like this:

Like Loading...

*Related*

chao ban 😀 ban hay giup minh chung minh mot bat dang thuc sau day:

cho cac so duong a , b , c thoa man chung minh rang neu ham

f la mot ham thoa man f”>0 va f(0)=0 thi ta nhan duoc bat dang thuc sau day:

sau khong co loi giai ???

Sorry my friend but i do not know Vietnamese, thus i cannot respond to your question.

Hello Mr !!! Now i want you prove the solution of the inequality below:

Let positive numbers (a , b) and (p, q) ; .

Prove that:

http://vankheakh.wordpress.com/2010/11/22/problem-68-van-khea/

Aw, this was an extremely nice post. Finding the time

and actual effort to make a really good article… but what can I say…

I procrastinate a lot and never manage to get anything done.