1. Cho a, b, c > 0.
C/m: $\frac{a^2}{b^{3}}+\frac{b^2}{c^{3}}+\frac{c^2}{a^{3}}\geq \frac{9}{a+b+c}$.
2. Cho x, y, z > 0.
C/m: $\frac{x^{4}}{y^{2}(x+z)}+\frac{y^{4}}{z^{2}(x+y)}+\frac{z^{4}}{x^{2}(y+z)}\geq \frac{x+y+z}{2}$.
3. Cho a, b, c là độ dài 3 cạnh của một tam giác.
C/m: $\sqrt{2}(a+b+c)\leq \sqrt{a^2+b^2}+\sqrt{b^2+c^2}+\sqrt{c^2+a^2}\leq \sqrt{3}(a+b+c)$.
4. Cho a, b, c > 0.
C/m: $\frac{a}{bc(c+a)}+\frac{b}{ac(a+b)}+\frac{c}{ab(b+c)}\geq \frac{27}{2(a+b+c)^2}$.