Question

if a=2+√3, then find value of 1/a​

Answer 1

Answer:

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

Answer 2

a = 2 + √3

1/a

= 1 / (2 + √3)

= (2 - √3) / (2 + √3) (2 - √3)

= (2 - √3) / (2)² - (√3)²

= (2 - √3) / 4 - 3

= (2 - √3)