1, Cho a,b,c đôi một khác nhau. C/m
$\frac{a^{3}-b^{3}}{(a-b)^{3}}+\frac{b^{3}-c^{3}}{(b-c)^{3}}+\frac{c^{3}-a^{3}}{(c-a)^{3}}$
2, cho $a,b,c\geq 0$ Cm
a, $\sqrt{a^{2}+ab+b^{2}}+\sqrt{b^{2}+bc+c^{2}}+\sqrt{c^{2}+ca+a^{2}}\geq \sqrt{3}(a+b+c)$
b, $\sum a(-\sqrt{a}+\sqrt{b}+\sqrt{c})\leq 3\sqrt{abc}$
3, cho a,b,c>0 Cm
$\frac{a^{8}+b^{8}+c^{8}}{a^{3}*b^{3}*c^{3}}\geq \frac{1}{a}+\frac{1}{b}+\frac{1}{c}$
4, cho a,b,c,d>0 Cm
$\frac{a+b}{a+b+c}+\frac{b+c}{b+c+d}+\frac{c+d}{c+d+a}+\frac{d+a}{d+a+b}< 3$