Question

Please Solve this
$x = 1 - \sqrt{2}$
Then Find
(X-1/X)³​

Answer 1

Answer:

8

Solution:

Given : x = 1 - √2

To find : (x - 1/x)³ = ?

We have ;

=> x = 1 - √2 ---------(1)

=> 1/x = 1/(1 - √2)

On rationalising the denominator of the term in RHS , We have ;

=> 1/x = (1 + √2) / (1 + √2)(1 - √2)

=> 1/x = (1 + √2) / [ 1² - (√2)² ]

=> 1/x = (1 + √2) / (1 - 2)

=> 1/x = (1 + √2) / (-1)

=> 1/x = - (1 + √2) -------(2)

Now, Using eq-(1) and (2) , we get ;

=> x - 1/x = (1 - √2) - [- (1 + √2)

=> x - 1/x = 1 - √2 + 1 + √2

=> x - 1/x = 2

=> (x - 1/x)³ = 2³ { cubing both sides }

=> (x - 1/x)³ = 8

Hence,

The required answer is 8 .