$1).$Cho $\left\{ \begin{array}{l} a,b,c>0\\ a^3+b^3+2c^3=1 \end{array} \right..$ Chứng minh:
$\frac{a^2}{b^3+2c^3}+\frac{b^2}{2c^3+a^3}+\frac{2c^2}{c^3+a^3+b^3}\geq \frac{4\sqrt[3]{4}}{3}$
$2).$Cho $\left\{ \begin{array}{l} a,b>0\\ a^2+b^2=\frac{2}{3}\end{array} \right..$ Chứng minh:$\frac{a}{1+3b^2}+\frac{b}{1+3a^2}\geq \frac{\sqrt{3}}{3}$