Question 182
Let $x$, $y$, $z$ be positive real numbers. 1. If $x + y + z \geq 3$, is it necessarily verified that $\frac{1}{x} + \frac{1}{y} + \frac{1}{z} \leq 3$? 2. If $x + y + z \leq 3$, is it necessarily verified that $\frac{1}{x} + \frac{1}{y} + \frac{1}{z} \geq 3$?