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.
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.
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?