OlympiadMediumInequalities10–12

What is the minimum value of $x + \frac{1}{x}$ for $x > 0$ ?

Qual é o valor mínimo de $x + \frac{1}{x}$ para $x > 0$ ?

Answer options

Solution

By AM-GM: $x + \frac{1}{x} \ge 2\sqrt{x \cdot \tfrac{1}{x}} = 2$ . Minimum when $x = 1$ .