Question

if a=2+√3 then find a-1/a​

Answer 1

I hope it helps you.

Answer 2

Answer:

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

$= \frac{1 + \sqrt{3} }{2 + \sqrt{3} }$

By rationalization;

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

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

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

$= \frac{ - ( 1 + 3 \sqrt{3} )}{ - 1}$

$= 1 + 3\sqrt{3}$