1. Bigger or equal to

Prove that 1/(a+b)+1/(b+c)+1/(a+c) is bigger or equal to 4.5 where a, b and c are positive and their sum 1.

codecogs

3. Re: Bigger or equal to

$a<=b<=c$

4. Re: Bigger or equal to

What do you mean?

5. Re: Bigger or equal to

minimum=4.5 when a=b=c=1/3

6. Re: Bigger or equal to

Originally Posted by DenisB
minimum=4.5 when a=b=c=1/3
While I agree with your answer Sir Denis I think you should demonstrate it is in fact a minimum!

7. Re: Bigger or equal to

Was leaving that for you Sir Roamsect...

8. Re: Bigger or equal to

Yeah, it has to be demonstrated.

9. Re: Bigger or equal to

Originally Posted by louis33
What do you mean?
I couldn't get my equations to display properly
I typed it all up but codecogs swallowed it
what is codecogs anyway?

now a+b is less than or equal to 2c and so on
next use the AM-GM inequality

try again

$\displaystyle a\leq b\leq c$

10. Re: Bigger or equal to

Originally Posted by Idea
I couldn't get my equations to display properly
I typed it all up but codecogs swallowed it
what is codecogs anyway?

now a+b is less than or equal to 2c and so on
next use the AM-GM inequality

try again

$\displaystyle a\leq b\leq c$
Do not use the [tex /tex] tags.