Question

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please give with steps i want steps only​

Answer 1

Step-by-step explanation:

Given :-

x = 1-√2

To find :-

Find the value of (x - 1/x )^3 ?

Solution:-

Given that:

x = 1-√2

1/x = 1/(1-√2)

The denominator = 1-√2

We know that

The Rationalising factor of a-√b = a+√b

The Rationalising factor of 1-√2 = 1+√2

On Rationalising the denominator then

=>1/(1-√2) × (1+√2)/(1+√2)

=> (1+√2)/(1-√2)(1+√2)

Denominator is in the form of (a+b)(a-b)

Where a = 1 and b = √2

We know that (a+b)(a-b)=a^2-b^2

=> (1+√2)/(1^2-(√2)^2)

=> (1+√2)/(1-2)

=> (1+√2)/-1

=> -(1+√2)

=> -1-√2

Therefore, 1/x = -1-√2

Now, x - 1/x

=>( 1-√2)-(-1-√2)

=> 1-√2+1+√2

=>(1+1)+(√2-√2)

=> 2+0

=2

Therefore , x- 1/x = 2

Now ,

[x-(1/x)]^3

=> 2^3

=> 2×2×2

=> 8

Answer:-

The value of [x-(1/x)]^3 for the given problem is 8

Used formulae:-

• (a+b)(a-b)=a^2-b^2

• The Rationalising factor of a-√b = a+√b