Question

if x=2+√3, find (x+1/x) answer 64​

Answer 1

Answer:

4

Step-by-step explanation:

$x = 2 + \sqrt{3} \\ \\ \frac{1}{x} = \frac{1}{2 + \sqrt{3} } \\ \\ = > \frac{1}{x} = \frac{1}{(2 + \sqrt{3} )} \times \frac{(2 - \sqrt{3}) }{(2 - \sqrt{3} )} \\ \\ = > \frac{1}{x} = \frac{2 - \sqrt{3} }{ {2}^{2} - { (\sqrt{3} )}^{2} } \\ \\ = > \frac{1}{x} = \frac{2 - \sqrt{3} }{1} \\ \\ = > \frac{1}{x} = 2 - \sqrt{3} \\ \\ = > x + \frac{1}{x} = (2 + \sqrt{3} ) + (2 - \sqrt{3} ) \\ \\ = > x + \frac{1}{x} = 4$

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