Question

if I give you x=2+√3 find x-1/x​

Answer 1

Answer:

$2 \sqrt{3}$

Step-by-step explanation:

Given,

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

Solution

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