Find the value of \(a\)
\[ \frac{6}{3\sqrt{2} – 2\sqrt{3}} = 3\sqrt{2} – a\sqrt{3} \]
Solution:
\[ \frac{6}{3\sqrt{2} – 2\sqrt{3}} \times \frac{3\sqrt{2} + 2\sqrt{3}}{3\sqrt{2} + 2\sqrt{3}} \]
\[ = \frac{6(3\sqrt{2} + 2\sqrt{3})}{(3\sqrt{2})^2 – (2\sqrt{3})^2} \]
\[ = \frac{6(3\sqrt{2} + 2\sqrt{3})}{18 – 12} \]
\[ = \frac{6(3\sqrt{2} + 2\sqrt{3})}{6} \]
\[ = 3\sqrt{2} + 2\sqrt{3} \]
Comparing with \(3\sqrt{2} – a\sqrt{3}\)
\[ 3\sqrt{2} + 2\sqrt{3} = 3\sqrt{2} – a\sqrt{3} \]
\[ 2\sqrt{3} = -a\sqrt{3} \Rightarrow a = -2 \]