Bài 1: a, b, c > 0. C/m:
$\frac{a^{3}}{a^{2}+b^{2}} + \frac{b^{3}}{b^{2}+c^{2}} + \frac{c^{3}}{c^{2}+a^{2}} \geq \frac{a+b+c}{2}$
Bài 2: a, b, c > 0. ab + bc + ca = 1. CMR:
$a^{2}+b^{2}+c^{2}+\frac{8abc}{(a+b)(b+c)(c+a)} \geq 2$
Bài 3: a, b, c > 0. CMR:
$\frac{a^{5}}{(b+c)^{3}} + \frac{b^{5}}{(c+a)^{3}} + \frac{c^{5}}{(a+b)^{3}} \geq \frac{a^{2}+b^{2}+c^{2}}{8}$
Bài 4: a, b, c > 0. CMR:
$\frac{a^{2}+b^{2}+c^{2}}{ab+bc+ca} + \frac{8abc}{(a+b)(b+c)(c+a)}$