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x - 1/x given, x > 0: find x + 1/x first, then x^n - 1/x^n

This type of question, asked 3 times: 17 Jul 2023 S2, 20 Jul 2023 S3, 20 Jul 2023 S4. All 3 questions below, oldest first.

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  1. Question 1

    17 Jul 2023 S2

    72
    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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  2. Question 2

    20 Jul 2023 S3

    72
    If (x−1x)=22\left(x - \frac{1}{x}\right) = 2\sqrt{2}, and x>1x > 1, what is the value of (x6−1x6)\left(x^6 - \frac{1}{x^6}\right)?

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  3. Question 3

    20 Jul 2023 S4

    53
    If (x−1x)=6\left(x - \frac{1}{x}\right) = 6, and x>0x > 0, find the value of (x2−1x2)\left(x^2 - \frac{1}{x^2}\right).

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