Find the value
\[ x = \sqrt{5} + 2 \]
Solution:
\[ \frac{1}{x} = \frac{1}{\sqrt{5} + 2} \times \frac{\sqrt{5} – 2}{\sqrt{5} – 2} \]
\[ = \frac{\sqrt{5} – 2}{5 – 4} = \sqrt{5} – 2 \]
\[ x – \frac{1}{x} = (\sqrt{5} + 2) – (\sqrt{5} – 2) \]
\[ = 4 \]
\[ \therefore \text{Correct Answer: } 4 \ (\text{Option b}) \]