với a, b, c > 0. CMR:

A= \(\dfrac{bc}{2a+b+c}+\dfrac{ca}{2b+c+a}+\dfrac{ab}{2c+a+b}\le\dfrac{a+b+c}{4}\)

với a, b, c > 0 và a+b+c=1. CMR:

\(\left(1+\dfrac{2}{1-a}\right)\left(1+\dfrac{2}{1-b}\right)\left(1+\dfrac{2}{1-c}\right)\ge64\)

cho a, b, c > 0 và \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=1\).

Tìm Max M = \(\dfrac{1}{\sqrt{1+a^2}}+\dfrac{1}{\sqrt{1+b^2}}+\dfrac{1}{\sqrt{1+c^2}}\)

cho a, b, c > 0 và \(a+b+c\ge3\). CMR :

A = \(\dfrac{\sqrt{a^2+1}}{b+c}+\dfrac{\sqrt{b^2+1}}{c+a}+\dfrac{\sqrt{c^2+1}}{a+b}\ge3\)