Question

Find the value of 'a' in the equation given below:

$\frac{3}{\sqrt{3}-\sqrt{2}}=a\sqrt{3}-b\sqrt{2}$

Answer 1

We rationalize the denominator,
$\frac{3}{\sqrt{3}-\sqrt{2}}\times \frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}+\sqrt{2}}$ $=\frac{3(\sqrt{3}+\sqrt{2})}{3-2}$
$=3\sqrt{3}+3\sqrt{2}$
$⟹a=3,b=-3$