a.$a^3+b^3$ \geq ab(a+b)
(a+b)($a^2-ab+b^2$) \geq ab(a+b)
$a^2-2ab+b^2$ \geq 0
$(a-b)^2$ \geq 0
dấu = xảy ra khi a=b
b.($\dfrac{a+b}{2})^2$ \geq $\dfrac{a^2+b^2}{2}$
$\frac{a^2+2ab+b^2}{4}$ \geq $\dfrac{a^2+b^2}{2}$
$\frac{a^2+2ab+b^2-2a^2-2b^2}{4}$ \geq 0
$\frac{-a^2+2ab-b^2}{4}$ \geq 0
$\frac{(-a-b)^2}{4}$ \geq 0
dấu = xảy ra khi a= b
(a+b)($a^2-ab+b^2$) \geq ab(a+b)
$a^2-2ab+b^2$ \geq 0
$(a-b)^2$ \geq 0
dấu = xảy ra khi a=b
b.($\dfrac{a+b}{2})^2$ \geq $\dfrac{a^2+b^2}{2}$
$\frac{a^2+2ab+b^2}{4}$ \geq $\dfrac{a^2+b^2}{2}$
$\frac{a^2+2ab+b^2-2a^2-2b^2}{4}$ \geq 0
$\frac{-a^2+2ab-b^2}{4}$ \geq 0
$\frac{(-a-b)^2}{4}$ \geq 0
dấu = xảy ra khi a= b
