Question

solve this question please

Answer 1

$\frac{3 + \sqrt{7} }{3 - \sqrt{7} } \times \frac{3 + \sqrt{7} }{3 + \sqrt{7} } = a + b \sqrt{7} \\ \frac{(3)^{2} + (\sqrt{7}) ^{2} + 2(3)( \sqrt{7} ) }{ {3}^{2} - ({ \sqrt{7} )}^{2} } = a + b \sqrt{7} \\ \frac{9 + 7 + 6 \sqrt{7} }{9 - 7} =a + b \sqrt{7}\\ \frac{16 + 6 \sqrt{7} }{2} =a + b \sqrt{7} \\ \frac{2(8 + 3 \sqrt{7}) }{2} = a + b \sqrt{7} \\ 8 + 3 \sqrt{7} = a + b \sqrt{7} \\ a = 8 \: \: \: \: and \: \: \: \: b = 3$