Question

if x=2- root 3 , find x-1/x

Answer 1

Step-by-step explanation:

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