Question

Please Answer the question attached below-question no.11

X=2+square root 3,find the value of (x-1/x)^2

Answer 1

Answer:

12

Solution:

Given : x = 2 + √3

To find : (x - 1/x)²

We have ,

x = 2 + √3

Thus,

1/x = 1/(2 + √3)

Now,

Rationalising the denominator of the term in RHS , we have ;

=> 1/x = (2 - √3) / (2 + √3)(2 - √3)

=> 1/x = (2 - √3) / {2² - (√3)²}

=> 1/x = (2 - √3) / (4 - 3)

=> 1/x = (2 - √3) / 1

=> 1/x = 2 - √3

This,

=> x - 1/x = ( 2 + √3) - (2 - √3)

=> x - 1/x = 2 + √3 - 2 + √3

=> x - 1/x = 2√3

=> (x - 1/x)² = (2√3)²

=> (x - 1/x)² = 12

Hence,

The required value of (x - 1/x)² is 12 .