Question

Solve this:-

$\frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5 - \sqrt{3} } } = a + \sqrt{3} b$

Answer 1

Heya

$\frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } = ( \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} })( \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} })$

$= \frac{ {( \sqrt{5} + \sqrt{3} )}^{2} }{ { \sqrt{5} }^{2} - { \sqrt{3} }^{2} } = \frac{8 + 2 \sqrt{15} }{2}$

$= 4 + \sqrt{15}$

Comparing this to ( a + b √3 ) :
$a = 4 \: \: b = \sqrt{5}$


Hope this helps ^_^