Question

If a=2+root 3 find a-1/a?

Answer 1

Given a = 2 + √3 ⇒ (1/a) = 1 / (2 + √3) Multiply and divide by (2 − √3) ⇒ (1/a) = (2 − √3) / [(2 + √3)(2 − √3)] ⇒ (1/a)  ...

Answer 2

$a = 2 + \sqrt{3} \\.. \frac{1}{a} = \frac{1}{2 + \sqrt{3} } \\ \: \: \: \: \: \: \: \: = \frac{1}{2 + \sqrt{3}} \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ \: \: \: \: \: \: \: = \frac{2 - \sqrt{3} }{1} \\ \: \: \frac{1}{a} = 2 - \sqrt{3} . \\ \\ now.... \\ a - \frac{1}{a} = (2 + \sqrt{3} ) - (2 - \sqrt{3} ) \\ \: \: \: \: \: \: \: \: \: \: \: \: = 2 + \sqrt{3} - 2 + \sqrt{3} \\ a - \frac{1}{a} = 2 \sqrt{3} .......$
Hope this helps