Can anyone help me prove this equation?

• Oct 23rd 2012, 09:21 PM
bxuan
Can anyone help me prove this equation?
Here's the problem: Sq root(ab) ≤ (a+b)/2

So I'm stuck here, how do I prove that a and b are positive real numbers? Should I go with a counterexample?
• Oct 23rd 2012, 10:23 PM
JJacquelin
Re: Can anyone help me prove this equation?
a= -1
b= -1
sqrt(ab)=sqrt(1)=1
(a+b)/2 = (-1-1)/2 = -1
sqrt(ab)>(a+b)/2
• Oct 24th 2012, 02:31 AM
Plato
Re: Can anyone help me prove this equation?
Quote:

Originally Posted by bxuan
Here's the problem: Sq root(ab) ≤ (a+b)/2
prove that a and b are positive real numbers?

It is true $(p-q)^2\ge 0$ so $p^2+q^2\ge 2pq$.

If $a>~\&~b>0$ then let $p=\sqrt{a}~\&~q=\sqrt{b}$.