happy bithday for all.

I hope you that help me to prove this inequalitie:

a,b,c are positiv reel

sqrt(2a/(a+b) + sqrt(2b/(b+c)+ sqrt(2c/(c+a)<3.

Thank you in advance.

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- Jan 4th 2011, 01:32 PMLamalifInequality Problem
happy bithday for all.

I hope you that help me to prove this inequalitie:

a,b,c are positiv reel

sqrt(2a/(a+b) + sqrt(2b/(b+c)+ sqrt(2c/(c+a)<3.

Thank you in advance. - Jan 4th 2011, 03:27 PMPlato
Suppose that each of $\displaystyle a,~b,~\&~c$ is a positive real numbers.

If $\displaystyle a=b=c$ then $\displaystyle \sqrt{\dfrac{2a}{a+b}}+\sqrt{\dfrac{2b}{b+c}} +\sqrt{\dfrac{2c}{a+c}}=3 $

If we have $\displaystyle a<b= c$ then $\displaystyle \sqrt{\dfrac{2a}{a+b}}+\sqrt{\dfrac{2b}{b+c}} +\sqrt{\dfrac{2c}{a+c}}<3 $.

WHY? - Jan 5th 2011, 08:32 AMLamalif
**Thank you Platon.**

I have an idea :

a/2<(a+b)/2 and 2/(a+b)<2/a and sqrt(2a/(a+b))<sqrt(2).

by this method we arrive at: sqrt(2a/(a+b))+sqrt(2b/(c+b))+sqrt(2c/(a+c)) <3sqrt(2).

Thank you again. - Jan 5th 2011, 08:36 AMalexmahone
- Jan 5th 2011, 08:51 AMLamalif