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x + 1/x given: value of a combination of power sums

This type of question, asked 3 times: 18 Sep 2025 S2, 19 Sep 2025 S1, 19 Sep 2025 S3. All 3 questions below, oldest first.

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  1. Question 1

    18 Sep 2025 S2

    56
    Given, x+1x=4x + \frac{1}{x} = 4, Find the value of: x6+1x6−3(x4+1x4)+4(x2+1x2)x^6 + \frac{1}{x^6} - 3\left(x^4 + \frac{1}{x^4}\right) + 4\left(x^2 + \frac{1}{x^2}\right)

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  2. Question 2

    19 Sep 2025 S1

    56
    If x+1x=−1x + \frac{1}{x} = -1, then compute: x4+1x4+2x2+2x2x^4 + \frac{1}{x^4} + 2x^2 + \frac{2}{x^2}.

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  3. Question 3

    19 Sep 2025 S3

    56
    Given: x+1x=−2x + \frac{1}{x} = -2, then determine the value of x6+1x6−3(x4+1x4)+4(x2+1x2)x^6 + \frac{1}{x^6} - 3\left(x^4 + \frac{1}{x^4}\right) + 4\left(x^2 + \frac{1}{x^2}\right).

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