Cho a;b;c>0.
1 Với a+b+c=1. CMR:$\frac{bc}{\sqrt{a+bc}}+\frac{ca}{\sqrt{b+ca}}+\frac{ab}{\sqrt{c+ab}}\leq \frac{1}{2}$
2. Với abc=1. CMR: a) $\frac{a^3}{(1+b)(1+c)}+\frac{b^3}{(1+c)(1+a)}+\frac{c^3}{(1+a)(1+b)}\geq \frac{3}{4}$
b) $\frac{1}{a^3(b+c)}+\frac{1}{b^3(c+a)}+\frac{1}{c^3(a+b)}\geq \frac{3}{2}$
3. Với abc=8. CMR:$\frac{1}{\sqrt{1+a^3}}+\frac{1}{\sqrt{1+b^3}}+\frac{1}{\sqrt{1+c^3}}\geq 1$