## Question

- Given that \(a > 0\), \(b > 0\), prove that
\[\begin{equation*}
\frac{a}{b} + \frac{b}{a} \ge 2.
\end{equation*}\]
- Given that \(x > 0\), \(y > 0\), \(z > 0\) and that \(x + y + z = 3\), prove that
\[\begin{equation*}
\frac{1}{x} + \frac{1}{y} + \frac{1}{z} \ge 3.
\end{equation*}\]