If $$x=2-\sqrt3$$​, then $$x - \frac{1}{x}$$​ is:

Correct option is C

Given:

​$$x = 2 - \sqrt{3}​$$​​

We need to find the value of $$x - \frac{1}{x}.$$​​

Solution:

​$$\frac{1}{x} = \frac{1}{2 - \sqrt{3}} \times \frac{2 + \sqrt{3}}{2 + \sqrt{3}} = \frac{2 + \sqrt{3}}{(2 - \sqrt{3})(2 + \sqrt{3})}$$=$$\frac{2+\sqrt3}{4- 3}$$​​

Thus, we have:

​$$\frac{1}{x} = 2 + \sqrt{3}$$​​

Now we can compute:

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

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

Option (C) is right.