Question

If x = 2 + √3, then find 1/x

Answer 1

Answer:

1 / x = ( 2 - √3 )

Step-by-step explanation:

Given----> x = 2 + √3

To find ---> Value of 1 / x.

Solution---> ATQ,

x = 2 + √3

Now we have to find value of 1 / x , which is reciprocal of x .

1 / x

Putting value of x in it , we get,

= 1 / ( 2 + √3 )

Now we rationalize the denominator by multiplying by the conjugate of denominator in the numerator and denominator which is

( 2 - √3 )

= ( 2 - √3 ) / ( 2 + √3 ) ( 2 - √3 )

We know that, a² - b² = ( a + b ) ( a - b ) , applying it here , we get,

= ( 2 - √3 ) / { ( 2 )² - ( √3 )² }

= ( 2 - √3 ) / ( 4 - 3 )

= ( 2 - √3 ) / 1

1 / x = ( 2 - √3 )

Additional information--->

1) ( a + b )² = a² + b² + 2ab

2) ( a - b )² = a² + b² - 2ab

3) a² - b² = ( a + b) ( a - b )

4) ( a + b )³ = a³ + b³ + 3ab ( a + b )

5) ( a - b )³ = a³ - b³ - 3ab ( a - b )