Question

find the following question
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Answer 1

Step-by-step explanation:

$a + b \sqrt{15} = \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \\ \\ solving \: \: r.h.s. = > \\ \\ = \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} } = \frac{ {( \sqrt{5} + \sqrt{3} )}^{2} }{5 - 3} = \frac{5 + 3 + 2 \sqrt{15} }{2} \\ \\ = \frac{8 + 2 \sqrt{15} }{2} = 4+ \sqrt{15} \\ \\ compare = > \\ \\ a = 4 \: \: \: \: and \: \: \: \: b = 1$