Question

If x= 2+√3, find x-1/x

Answer 1

when x= 2+√3

therefore substituting in x-1/x

(2+√3) - 1/(2-√3)

(2+√3)(2-√3)-1/(2-√3)

2²+√3²-1/(2-√3)

4-3-1/2-√3

0/2-√3

0

Thank you!☘️

All the best.☺️

#HAKUNA MATATA @Akshaymas.

Answer 2

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

x - 1/x = (2 + root3) - ( 2- root 3)

x - 1/x = 2 + root3 - 2 + root3

$x - \frac{1}{x} = 2 \sqrt{3}$