Question 100
Show that for all positive real numbers $x$, $y$ and $z$ the following inequality is held:
$$
\frac{x(2x - y)}{y(2z + x)} + \frac{y(2y - z)}{z(2x + y)} + \frac{z(2z - x)}{x(2y + z)} \ge 1
$$
$$
\frac{x(2x - y)}{y(2z + x)} + \frac{y(2y - z)}{z(2x + y)} + \frac{z(2z - x)}{x(2y + z)} \ge 1
$$