Question

if a=2+√3 then the value of 1/a is​

Answer 1

Answer:-

Given:-

$a = 2 + \sqrt{3}$

To Find:-

$\frac{1}{a}$

By The Problem:-

$a = 2 + \sqrt{3}\\ \frac{1}{a} = \frac{1}{2+\sqrt{3} } \\ \frac{1}{a} = \frac{1×(2-\sqrt{3} )}{(2+\sqrt{3} )(2-\sqrt{3} )}\\ \frac{1}{a} = \frac{2 - \sqrt{3} }{1} \\ = > \frac{1}{a} = 2 - \sqrt{3}(Answer)$

Solve by Rationalization of denominator.

Answer 2

Answer:

2 - √3

Step-by-step explanation:

Given,

a = 2 + √3

1 / a

= 1 / ( 2 + √3 )

= ( 2 - √3 ) / ( 2 + √3 ) ( 2 - √3 )

= ( 2 - √3 ) / ( 2² - √3² )

= ( 2 - √3 ) / ( 4 - 3 )

= ( 2 - √3 ) / 1

= 2 - √3