Question

if x=2+√3 find (x+1/x) ^3​

Answer 1

Step-by-step explanation:

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

$({x + \frac{1}{x}) }^{3} \\ {((2 + \sqrt{3}) + (2 - \sqrt{3)} )}^{3} \\ {4}^{3} \\ 64$

hence answer is 64

:)