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x + 1/x given: find x^3 + 1/x^3 or x^6 + 1/x^6 by the cube identity

This type of question, asked 6 times: 14 Jul 2023 S3, 24 Jul 2023 S2, 24 Jul 2023 S3, 25 Jul 2023 S3, 19 Sep 2024 S1, 14 Sep 2025 S1. All 6 questions below, oldest first.

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  1. Question 1

    14 Jul 2023 S3

    63
    If x+1x=7x + \frac{1}{x} = 7, then the value of x6+1x6x^6 + \frac{1}{x^6} is:

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  2. Question 2

    24 Jul 2023 S2

    66
    If (x+1x)=22\left(x + \frac{1}{x}\right) = 2\sqrt{2}, what is the value of (x6+1x6)\left(x^6 + \frac{1}{x^6}\right)?

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  3. Question 3

    24 Jul 2023 S3

    71
    If sin⁡θ+cosecθ=5\sin\theta + \text{cosec}\theta = \sqrt{5}, then the value of sin⁡3θ+cosec3θ=\sin^3\theta + \text{cosec}^3\theta = ________.

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  4. Question 4

    25 Jul 2023 S3

    56
    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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  5. Question 5

    19 Sep 2024 S1

    74
    If (a+1a)=73\left(a + \frac{1}{a}\right) = 7\sqrt{3}, then what is the value of (a6+a−6)(a^6 + a^{-6})?

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  6. Question 6

    14 Sep 2025 S1

    74
    Given, x+1x=4x + \frac{1}{x} = 4 find the value of x3+1x3x^3 + \frac{1}{x^3}.

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