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x + 1/x = k, x > 1: find x^8 - 1/x^8

The same question, asked 3 times: 18 Jul 2023 S3*, 20 Jul 2023 S4*, 26 Jul 2023 S3. Every wording below, oldest first.

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  1. Question 1

    18 Jul 2023 S3

    73
    If (x+1x)=5\left(x + \frac{1}{x}\right) = 5, and x>1x > 1, what is the value of (x8−1x8)\left(x^8 - \frac{1}{x^8}\right)?

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  2. Question 2

    20 Jul 2023 S4

    60
    If (x+1x)=32\left(x + \frac{1}{x}\right) = 3\sqrt{2}, and x>1x > 1, what is the value of (x8−1x8)\left(x^8 - \frac{1}{x^8}\right)?

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  3. Question 3

    26 Jul 2023 S3

    69
    If (x+1x)=6\left(x + \frac{1}{x}\right) = \sqrt{6}, and x>1x > 1, what is the value of (x8−1x8)\left(x^8 - \frac{1}{x^8}\right)?

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