Question

If x = 1 - root2, find the value of (x-1/x)^3 ​

Answer 1

Answer:

(x - 1/x)³ = 8

Solution:

• Given : x = 1 - √2
• To find : (x - 1/x)³ = ?

We have ;

x = 1 - √2

Thus,

1/x = 1/(1 - √2)

Now,

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

=> 1/x = (1 + √2) / (1 - √2)(1 + √2)

=> 1/x = (1 + √2) / (1² - √2²)

=> 1/x = (1 + √2) / (1 - 2)

=> 1/x = (1 + √2) / (-1)

=> 1/x = - (1 + √2)

Now,

=> x - 1/x = (1 - √2) - [ - (1 + √2) ]

=> x - 1/x = 1 - √2 + 1 + √2

=> x - 1/x = 2

Now,

Cubing both the sides , we get ;

=> (x - 1/x)³ = 2³

=> (x - 1/x)³ = 8

Hence , (x - 1/x)³ = 8

Answer 2

Step-by-step explanation:

this is your answer dear friend