Question

Find the value of 'a' in the following equation:

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

Answer 1

We rationalize the denominator,
$\therefore \frac{2+\sqrt{3}}{2-\sqrt{3}}\times \frac{2+\sqrt{3}}{2+\sqrt{3}}$
$=\frac{4+3+4\sqrt{3}}{4-3}$
$=7+4\sqrt{3}$
$⟹a=7,b=4$