1. Cho a, b, c >0. Chứng minh rằng:
$\frac{a}{2a +b +c} + \frac{b}{a + 2b +c} + \frac{c}{a +b +2c} \leq \frac{3}{4}$
2. Cho a, b, c > 0. Tìm Min:
$S = \frac{a^{3}}{b^{2}} + \frac{b^{3}}{c^{2}} + \frac{c^{3}}{a^{2}} + 27\left ( \frac{1}{ab} + \frac{1}{bc} + \frac{1}{ac} \right )$
3. Cho a, b > 0. Tìm Min:
$S = \frac{a +b }{\sqrt{ab}} + \frac{\sqrt{ab}}{ a +b }$
4. Cho $a \geq 2$ . Tìm Min:
$S = a + \frac{1}{a^{2}}$
5. Cho a, b > 0; $a + b \leq 1$ .Tìm Min:
$S = \frac{1}{a^{2} + b ^{2}} + \frac{1}{ab} + 4ab$