Question

plz solve it!
correct answer will get brain listed ​

Answer 1

$\bf \frac{5 + \sqrt{3} }{5 - \sqrt{3} } = \frac{a}{2} + \small3b \sqrt{15} \\ \\ \bf \frac{5 + \sqrt{3} }{5 - \sqrt{3} } \times \frac{5 + \sqrt{3} }{5 + \sqrt{3} } = \frac{a}{2} + \small3b \sqrt{15} \\ \\ \bf \frac{( {5 + \sqrt{3} )}^{2} }{ {5}^{2} - { \sqrt{3} }^{2} } = \frac{a}{2} + \small3b \sqrt{15} \\ \\ \bf \frac{28 + 10\sqrt{3} }{2} = \frac{a + \small6b \sqrt{5} \sqrt{3} } {2} \\ \\ \bf28 + 10\sqrt{3} ={a + \small6b \sqrt{5} \sqrt{3} } \\ \\ \large \red{\boxed{ \begin{array}{c} \sf \: a = 28 \\ \\ \sf \small 6b \sqrt{5} \sqrt{3} = 10 \sqrt{3} \\ \sf \: b = \frac{ \sqrt{5} }{3} \end{array}}}$