Question

If a = 2 + √3, find the value of a -
1
/a​

Answer 1

$\huge \color{aqua} {\underbrace {\boxed {\colorbox{black}{answer}}}}$

Step-by-step explanation:

$a = 2 + \sqrt{3} \\ a = 2 + \sqrt{3} \: \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ a = \frac{ {(2)}^{2} - ( { \sqrt{3}) }^{2} }{2 - \sqrt{3} } \\ a = \frac{4 - 3}{2 - \sqrt{3} } \\ a = \frac{1}{2 - \sqrt{3} } \\ \\ therefore : \\ a - \frac{1}{a} \\ = \frac{1}{2 - \sqrt{3} } - \frac{1}{ \frac{1}{2 - \sqrt{3} } } \\ = \frac{1}{2 - \sqrt{3} } - \frac{2 - \sqrt{3} }{1} \\ = \frac{1}{1} \\ = 1ans:$

$\huge \color{silver} {\underbrace {\boxed {\colorbox{black}{thnq}}}}$