Question

if a=6+2√3 than find a+1/a​

Answer 1

$x = 6 + 2 \sqrt{3} \\ \frac{1}{x} = \frac{1}{6 + 2 \sqrt{3} } \times \frac{6 - 2 \sqrt{3} }{6 - 2 \sqrt{3} } \\ \frac{1}{x} = \frac{6 - 2 \sqrt{3} }{ {6}^{2} - {(2 \sqrt{3}) }^{2} } \\ \frac{1}{x} = \frac{6 - 2 \sqrt{3} }{36 - 12} \\ \frac{1}{x} = \frac{6 - 2 \sqrt{3} }{24} \\ x + \frac{1}{x} = 6 + 2 \sqrt{3} + \frac{6 - 2 \sqrt{3} }{24} = \\ \frac{144 + 48 \sqrt{3} + 6 - 2 \sqrt{3} }{24} = \frac{150 + 46 \sqrt{3} }{24}$