Question

hlw✋ everyone
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If x=1-root2,find the value of (x-1/x)^4

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Answer 1

Answer:

= [x - (1/x)]³ → where: x = 1 + √2

= [(1 + √2) - { 1/(1 + √2) } ]³

= [ { (1 + √2)² - 1 } / (1 + √2) ]³

= [ { (1 + 2√2 + 2) - 1 } / (1 + √2) ]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

Answer:

16

Step-by-step explanation:

Given x = 1 - √2

(1/x) = (1/1 - √2) * (1 + √2/1 + √2)

      = (1 + √2)/(1)² - (√2)²

      = (1 + √2)/-1

      = -1 - √2

Now,

x - 1/x = 1 - √2 - (1 - √2)

          = 1 - √2 - 1 + √2

         = 2

Therefore,

(x - 1/x)⁴

⇒ (2)⁴

⇒ 16

Hope it helps!