Question

please solve this question

Answer 1

Hope it will help you .

Answer 2

$Given \: :- \\ \\ \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5 } - \sqrt{3} } = a + b \sqrt{15}$

Rationalizing LHS we get

$\frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} } \\ \\ = \frac{ (\sqrt{5} + \sqrt{3}) {}^{2} }{ (\sqrt{5}) {}^{2} - (\sqrt{3} ) { }^{2} } \\ \\ \ = \frac{5 + 3 + 2 \sqrt{15} }{5 - 3 } \\ \\ = \frac{8 + 2 \sqrt{15} }{2} \\ \\ = 4 + \sqrt{15}$

Comparing LHS with RHS

$4 + \sqrt{15} = a + b \sqrt{15} \\ \\since \: LHS \: = RHS \: \\ \\ we \: get \\ \\ a = 4 \: and \: \\ b = 1$

HOPE THAT HELPES!!