Mai Pham

Cho x, y, z>0 thỏa mãn xyz = 1

Tìm min $\frac{x^{2}}{x + y + y^{3}z} + \frac{y^{2}}{y + z + z^{3}x} +\frac{z^{2}}{x + z + x^{3}y}$

Cho a, b, c >0 thỏa mãn $a^{2} + b^{2} + c^{2} = 3$

Chứng minh $\frac{a}{a^{2} + 2b + 3} + \frac{b}{b^{2} + 2c + 3} + \frac{c}{c^{2} + 2a + 3} \leqslant \frac{1}{2}$

Cho a, b, c > 0. Chứng minh $\sqrt{\frac{a}{b + c}} + \sqrt{\frac{b}{a + c}} + \sqrt{\frac{c}{a + b}} > 2$

Cho x, y, z > 0. Chứng minh  $\dpi{100} \left ( 1 + \frac{x}{y} \right )\left ( 1 + \frac{y}{z} \right )\left ( 1 + \frac{z}{x} \right ) \geqslant 2 + \frac{2\left ( x + y + z \right )}{\sqrt[3]{xyz}}$