Cho a, b, c dương. Chứng minh
1) $\frac{{{a}^{3}}}{{{b}^{2}}+{{c}^{2}}}+\frac{{{b}^{3}}}{{{c}^{2}}+{{a}^{2}}}+\frac{{{c}^{3}}}{{{a}^{2}}+{{b}^{2}}}\ge \frac{a+b+c}{2}$
2) $\frac{{{a}^{2}}}{a+cb}+\frac{{{b}^{2}}}{b+ca}+\frac{{{c}^{2}}}{c+ab}\ge \frac{a+b+c}{4}$, (với ab+bc+ca=abc)