Question 96
Let $a$ and $b$ be positive real numbers such that
$$
\frac{a}{b} + \frac{b}{a} = 3 \quad \text{and} \quad \frac{a^2}{b} + \frac{b^2}{a} = 10.
$$
Determine $\frac{1}{a} + \frac{1}{b}$.
(Kristina Ana Škreb)
$$
\frac{a}{b} + \frac{b}{a} = 3 \quad \text{and} \quad \frac{a^2}{b} + \frac{b^2}{a} = 10.
$$
Determine $\frac{1}{a} + \frac{1}{b}$.
(Kristina Ana Škreb)