Question

please tell me the working.

Answer 1

Step-by-step explanation:

a = 2 + √3

$\frac{1}{a} = \frac{1}{2 + \sqrt{3} } \\ \\ = \frac{2 - \sqrt{3} }{ {2}^{2} - { \sqrt{3} }^{2} } \\ \\ = \frac{2 - \sqrt{3} }{4 - 3} \\ \\ = 2 - \sqrt{3}$

$\bf \: a - \cfrac{1}{a} = 2 + \sqrt{3} - (2 - \sqrt{3} ) \\ \\ \bf = 2 + \sqrt{3} - 2 + \sqrt{3} \\ \\ = \bf \: 2 \sqrt{3}$

Answer 2

$answer = 2 \sqrt{3}$

$step \: by \: step \: explaination$

$given \: that \\ a = 2 + \sqrt{3} \\ then \: \: value \: of \\ a - \frac{1}{a} = 2 + \sqrt{3} - \frac{ 1}{2 + \sqrt{3} } \\ = 2 \times \sqrt{3} - \frac{1}{2 + \sqrt{3} } \times \\ \frac{ 2 - \sqrt{3} }{2 - \sqrt{3} } \: \: on \: \: rationalize \\ 2 + \sqrt{3} - \frac{(2 - \sqrt{3}) }{4 - 3} \\ 2 + \sqrt{3} - 2 + \sqrt{3} \\ 2 \sqrt{3}$