Question

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

Answer 1

$a = 2 + \sqrt{3}$

$a - \frac{1}{a} \\ \\ = 2 + \sqrt{3} - \frac{1}{2 + \sqrt{3} } \\ \\ = \frac{4 + 3 + 4 \sqrt{3} - 1 }{2 + \sqrt{3} } \\ \\ = \frac{6 + 4 \sqrt{3} }{2 + \sqrt{3} } \\ \\ = \frac{2(3 + 2 \sqrt{3}) }{2 + \sqrt{3} }$

Answer 2

Step-by-step explanation:

(2+√3)-1/(2+√3)

taking LCM of both

[(2+√3)(2+√3)-1]/(2+√3)

2+√3 will cancel out

then we get

2+√3-1

= 1+√3

answer = 1+√3