Question

hey guys plzz help me
x=2+√3 findx-1/x​

Answer 1

$\sf given \: x = 2 + \sqrt{3} \\ \\ \sf \therefore \frac{1}{x} = \frac{1}{2 + \sqrt{3} } \\ \\ \sf on \: rationalising \\ \\ \sf = \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ \\ \sf = \frac{2 - \sqrt{3} }{(2 + \sqrt{3} )(2 - \sqrt{3}) } \\ \\ \sf = \frac{2 - \sqrt{3} }{ {(2)}^{2} - ( { \sqrt{3} })^{2} } \\ \\ \sf = \frac{2 - \sqrt{3} }{4 - 3} \\ \\ \sf = 2 - \sqrt{3}$

therefore x - 1/x = (2 + √3) - (2 - √3)

= 2 + √3 - 2 + √3

= 2 - 2 + √3 + √3

= 2√3