Question

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

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

Answer 1

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