Question

if x=5-root21by 2 find the value of x+1/x

Answer 1

$x = \frac{5 - \sqrt{21} }{2} \\ therefore \: \frac{1}{x} = \frac{2}{5 - \sqrt{21} } \\ = \frac{2(5 + \sqrt{21)} }{(5 - \sqrt{21} )(5 + \sqrt{21)} } \\ = \frac{2(5 + \sqrt{21})}{25 - 21} = \frac{5 + \sqrt{21} }{2}$
$then \: x + \frac{1}{x} = \frac{5 - \sqrt{21} }{2} + \frac{5 + \sqrt{21} }{2} = 5$

Answer 2

the answer is x+1/x=529/10√21