Question

if a is equal to 2 + root 3 then find the value of a-1/a​

Answer 1

Step-by-step explanation:

$a = 2 + \sqrt{3} ; \\ \frac{a - 1}{a} = \frac{2 + \sqrt{3} - 1}{2 + \sqrt{3} } \\ = \frac{1 + \sqrt{3} }{2 + \sqrt{3} } \\ rationalize \: denominator \\ = \frac{(1 + \sqrt{3})(2 - \sqrt{3} }{(2 + \sqrt{3})(2 - \sqrt{3}) } \\ = \frac{2 - \sqrt{3} + 2 \sqrt{3} - 3 }{ {2}^{2} - {( \sqrt{3}) }^{2} } \\ = \frac{ - 1 + \sqrt{3} }{4 - 3} \\ = \frac{ - 1 + \sqrt{3} }{1} \\ = - 1 + \sqrt{3}$

Thanks for the question bro ❤️❣️✅✌️✌️✍️