Question

If x=5+2√6 then find x+1/x

Answer 1

Answer:

$x = 5 + 2 \sqrt{6} \\ \frac{x + 1}{x} = 1 + \frac{1}{x} \\ now \: \frac{1}{x} = \frac{1}{5 + 2 \sqrt{6} } \\ = \frac{1}{5 + 2 \sqrt{6} } \times \frac{5 - 2 \sqrt{6} }{5 - 2 \sqrt{6} } \\ = \frac{ {5 - 2 \sqrt{6} }^{2} }{ {5}^{2} - {2 \sqrt{6} }^{2} } \\ = \frac{25 + 24 - 10 \sqrt{6} }{25 - 24} = \frac{39}{1} \\ = 39 \\ hence \: \frac{x + 1}{x} = 1 + \frac{1}{x} \\ = 5 + 2 \sqrt{6} + 39 \\ = 44 + 2 \sqrt{6}$