Find the values of \(A\) and \(B\)
\[ \frac{1}{\sqrt{9} – \sqrt{8}} = A + B\sqrt{2} \]
Solution:
\[ \sqrt{9} = 3,\quad \sqrt{8} = 2\sqrt{2} \]
\[ \frac{1}{3 – 2\sqrt{2}} \times \frac{3 + 2\sqrt{2}}{3 + 2\sqrt{2}} \]
\[ = \frac{3 + 2\sqrt{2}}{9 – 8} \]
\[ = 3 + 2\sqrt{2} \]
Comparing with \(A + B\sqrt{2}\)
\[ A = 3,\quad B = 2 \]