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x - 1/x given: find an even-power sum x^4 + 1/x^4 or x^6 + 1/x^6

This type of question, asked 4 times: 21 Jul 2023 S2, 25 Jul 2023 S1, 26 Jul 2023 S3, 15 Sep 2025 S3. All 4 questions below, oldest first.

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  1. Question 1

    21 Jul 2023 S2

    67
    If (x−1x)=22(x - \frac{1}{x}) = 2\sqrt{2}, what is the value of (x6+1x6)(x^6 + \frac{1}{x^6})?

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  2. Question 2

    25 Jul 2023 S1

    65
    If (y−1y)=4\left(y - \frac{1}{y}\right) = 4, find the value of (y6+1y6)\left(y^6 + \frac{1}{y^6}\right).

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  3. Question 3

    26 Jul 2023 S3

    74
    If (x−1x)=10\left(x - \frac{1}{x}\right) = 10, what is the value of (x4+1x4)\left(x^4 + \frac{1}{x^4}\right)?

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  4. Question 4

    15 Sep 2025 S3

    74
    Given, x−1x=3x - \frac{1}{x} = 3, find the value of x4+1x4x^4 + \frac{1}{x^4}.

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