Cho x, y, z > 0 . CMR :

A= \(\dfrac{x^3}{zy}+\dfrac{y^3}{xz}+\dfrac{z^3}{xy}\ge x+y+z\)

Cho a, b, c > 0 . CMR:

A= \(\dfrac{1}{a^3+b^3+abc}+\dfrac{1}{b^3+c^3+abc}+\dfrac{1}{c^3+a^3+abc}\le\dfrac{1}{abc}\)

Cho a, b, c, d > 0 và \(ab+bc+cd+da=1\) . CMR:

A= \(\dfrac{a^3}{b+c+d}+\dfrac{b^3}{a+c+d}+\dfrac{c^3}{a+b+d}+\dfrac{d^3}{a+b+c}\ge\dfrac{1}{3}\)

Với x, y, z > 0 và xyz = 1 . CMR :

A= \(\dfrac{x^3}{\left(1+y\right)\left(1+z\right)}+\dfrac{y^3}{\left(1+x\right)\left(1+z\right)}+\dfrac{z^3}{\left(1+x\right)\left(1+y\right)}\ge\dfrac{3}{4}\)

với \(a_1\), \(a_2\), ... , \(a_n\) \(>0\) . CMR :

A= \(\dfrac{1}{a_1}+\dfrac{1}{a_2}+...+\dfrac{1}{a_n}\ge\dfrac{n^2}{a_1+a_2+...+a_n}\)

cho a, b, c > 0 và \(a+2b+3c\ge10\). CMR:

A= \(a+b+c+\dfrac{3}{4a}+\dfrac{9}{8b}+\dfrac{1}{c}\ge\dfrac{13}{2}\)