Question

Find the value of (x - 1/x)^3 if x = 1+√2

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Answer 1

Step-by-step explanation:

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Answer 2

Answer:

20-14√2

Step-by-step explanation:

according to question,

[(1+√2-1)/(1+√2)]^3

[√2/(1+√2)]^3

rationalising,

[√2(1-√2)/(1+√2)(1-√2)]^3 {(a+b)(a-b) = a^2 - b^2}

[√2-2/1-2]^3

[√2-2/(-1)]^3

[-(√2-2)]^3

[2-√2]^3 {(a-b)^3=a^3-b^3-3ab(a-b)}

2^3-√2^3-3(2√2)(2-√2)

8-(2√2)-6√2(2-√2)

8-2√2-12√2+12

8-14√2+12

20-14√2(answer)