Question

if a= 2-√3 then find the value of a-1/a​

Answer 1

$a = 2 - \sqrt{3}$

So,

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

Hence,

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

Answer 2

$\Huge \mathsf {\colorbox{yellow} {\underline{QUESTION}}}$

a= 2-√3 then find the value of

$if \: a = 2 - \sqrt{3 . }then \: find \: the \: value \: of \: \: a - \frac{1}{a}$

$\Huge \mathsf {\colorbox{yellow} {\underline{To Find}}}$

$find \: the \: value \: of \: a - \frac{1}{a}$

$\Huge \mathsf {\colorbox{yellow} {\underline{ANSWER}}}$

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

$2 - \sqrt{3} - \frac{1}{2 - \sqrt{3} } \times \frac{ 2 + \sqrt{3} }{2 + \sqrt{3} } by \: rationalizing$

$2 - \sqrt{3} - \frac{2 + \sqrt{3} }{4 - 3}$

$2 - \sqrt{3} - 2 - \sqrt{3}$

$2 - \sqrt{3} - 2 - \sqrt{3}$

So, Answer is -2√3