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x + 1/x given: find x^2 + 1/x^2 or x^4 + 1/x^4 by squaring

This type of question, asked 6 times: 17 Jul 2023 S4, 24 Jul 2023 S4, 10 Sep 2024 S1, 10 Sep 2024 S2, 13 Sep 2025 S2, 18 Sep 2025 S2. All 6 questions below, oldest first.

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  1. Question 1

    17 Jul 2023 S4

    61
    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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  2. Question 2

    24 Jul 2023 S4

    74
    If x+1x=9x + \frac{1}{x} = 9, then find x4+1x4x^4 + \frac{1}{x^4}.

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  3. Question 3

    10 Sep 2024 S1

    68
    If a+1a=12a + \frac{1}{a} = 12, then find the value of a2+1a2a^2 + \frac{1}{a^2}.

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  4. Question 4

    10 Sep 2024 S2

    63
    If x+1x=7\sqrt{x} + \frac{1}{\sqrt{x}} = 7, then the value of x+1xx + \frac{1}{x} is equal to:

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  5. Question 5

    13 Sep 2025 S2

    75
    Given, x+1x=5x + \frac{1}{x} = 5, then determine the value of x2+1x2x^2 + \frac{1}{x^2}.

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  6. Question 6

    18 Sep 2025 S2

    71
    Given, x+1x=4\sqrt{x} + \frac{1}{\sqrt{x}} = 4, then what is x+1xx + \frac{1}{x}?

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