Question

x =2- in root 3
then
x-1/x=?

Answer 1

heya , hope it helps , u can simplify it further !

Answer 2

Heya !!!

Identity used :

$(x + y)(x - y) = {x}^{2} - {y}^{2}$


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

On rationalizing the denominator we get,

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

Putting the values in (x) - (1/x) we get


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

Hope this helps ☺