Question

If x =1- √2,
find the value of( x-1/x)^3​

Answer 1

Answer:

8

Step-by-step explanation:

Given------> x = ( 1 - √2 )

To find-------> Value of ( x - 1 / x )³

Solution-------> ATQ,

x = ( 1 - √2 )

=> 1 / x = 1 / ( 1 - √2 )

Multiplying in numerator and denominator by the conjugate of denominator

= ( 1 + √2 ) / ( 1 - √2 ) ( 1 + √2 )

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

= ( 1 + √2 ) / ( 1 )² - ( √2 )²

= ( 1 + √2 ) / ( 1 - 2 )

= ( 1 + √2 ) / ( - 1 )

= - ( 1 + √2 )

= - 1 - √2

Now,

( x - 1 / x ) = ( 1 - √2 ) - ( - 1 - √ 2 )

= ( 1 - √2 + 1 + √2 )

= 2

=> ( x - 1 / x )³ = ( 2 )³

=> ( x - 1 / x )³ = 8