Question

If X=1-root2 find the value of (X-1/X)³​

Answer 1

Answer:

[x - (1/x)]^3 = [(x^2 - 1)/x]^3 = [((1 + 2√2 + 2) - 1)/(1 + √2)]^3 =

[x - (1/x)]^3 = [(x^2 - 1)/x]^3 = [((1 + 2√2 + 2) - 1)/(1 + √2)]^3 = [(2 + 2√2) / (1 + √2)]^3 = [(2(1 + √2)) / (1 + √2)]^3 = [2]^3 = 8

Answer 2

Solution

Given :-

• x = (1 -√2)

Find :-

• Value of (x - 1/x)³

Step - by - Step - Explanation

Now, calculate 1/x

➡ 1/x = 1/(1-√2)

Rationalize Denominator

➡ 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, Calculate (x - 1/x)³

➡(x - 1/x)³ =

➡ [ ( 1 - √2) - {-(1+√2)}]³

➡[(1 - √2 + 1 - √2)]³

➡ [ ( 2 )]³

➡8

Hence

• Value of (x - 1/x)³ = 8

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