Inegalitate.
Posted: Fri Jun 11, 2010 3:02 pm
Sa se demonstreze inegalitatea: \( \frac{x^{3}}{y^{3}}+\frac{y^{3}}{z^{3}}+\frac{z^{3}}{x^{3}}\ge\frac{1}{2}\left(\frac{x^{2}}{yz}+\frac{y^{2}}{zx}+\frac{z^{2}}{xy}\right)+\frac{3}{2},\ \forall x,\ y,\ z\in\left(0,\ +\infty\right) \).