Question

please help
Solve the answer​

Answer 1

$\huge{\underline{\underline{\mathtt{\purple{༒♛么}\pink{ᮘ}\green{S}\blue{W}\red{E}\orange{R♛༒}}}}}$

$\frac{2 \sqrt{5} + \sqrt{3} }{2 \sqrt{5} - \sqrt{3} } + \frac{2 \sqrt{5} - \sqrt{3} }{2 \sqrt{5} + \sqrt{3} } = a + b \sqrt{15} \\ \implies \frac{( {2 \sqrt{5} + \sqrt{3} })^{2} + ( {2 \sqrt{5 } - \sqrt{3} })^{2} }{(2 \sqrt{5}) ^{2} - ( { \sqrt{ 3} })^{2} } = a + b \sqrt{15} \\ \implies \frac{2(20 + 3)}{20 - 3} =a + b \sqrt{15} \\ \implies \: \frac{46}{17} = a + \sqrt{15} b \\ comparing \: coefficients \: we \: get \\ a = \frac{46}{17} \: \: \: b = 0$