Find the value of \( \frac{1}{x} \)
\[ x = \sqrt{2} – 1 \]
Solution:
\[ \frac{1}{x} = \frac{1}{\sqrt{2} – 1} \times \frac{\sqrt{2} + 1}{\sqrt{2} + 1} \]
\[ = \frac{\sqrt{2} + 1}{2 – 1} \]
\[ = \sqrt{2} + 1 \]
\[ x = \sqrt{2} – 1 \]
\[ \frac{1}{x} = \frac{1}{\sqrt{2} – 1} \times \frac{\sqrt{2} + 1}{\sqrt{2} + 1} \]
\[ = \frac{\sqrt{2} + 1}{2 – 1} \]
\[ = \sqrt{2} + 1 \]