# Given that $a, b > 0$, can we prove that $a/b + b/a \ge 2$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource
1. Given that $a > 0$, $b > 0$, prove that $\begin{equation*} \frac{a}{b} + \frac{b}{a} \ge 2. \end{equation*}$
2. Given that $x > 0$, $y > 0$, $z > 0$ and that $x + y + z = 3$, prove that $\begin{equation*} \frac{1}{x} + \frac{1}{y} + \frac{1}{z} \ge 3. \end{equation*}$