Question

if x is equal to 2 + root 2 root 3 find x -1/x

Answer 1

x = 2 + √2√3

x = 2 + √6
_________

$\frac{1}{x} = \frac{1}{2 + \sqrt{6} }$

By Rationalization,

$\frac{1}{x} = \frac{2 - \sqrt{6} }{2^2 - (\sqrt{6})^2 }$

$\frac{1}{x} = \frac{2- \sqrt{6} }{4 - 6}$

$\frac{1}{x} = \frac{2 - \sqrt{6} }{-2}$

1/x =  -1  +  √6/2

___________________

x -1/x = 2+√6  - ( -1 + √6/2 )

x-1/x = 2 + √6 + 1 - √6/2



i hope this will help you


-by ABHAY