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Quadratic x^2 - kx +/- 1 = 0: divide by x to get x +/- 1/x

This type of question, asked 3 times: 19 Jul 2023 S3, 25 Jul 2023 S1, 26 Jul 2023 S1. All 4 questions below, oldest first.

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  1. Question 1

    19 Jul 2023 S3

    64
    If x2−7x+1=0x^2 - 7x + 1 = 0, and 0<x<10 < x < 1, what is the value of x2−1x2x^2 - \frac{1}{x^2}?

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  2. Question 2

    25 Jul 2023 S1

    75
    If x2−15x+1=0x^2 - 15x + 1 = 0, what is the value of x4−223x2+6x^4 - 223x^2 + 6?

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  3. Question 3

    26 Jul 2023 S1

    74
    If x=1x−3x = \frac{1}{x - 3}, (x>0)(x > 0), then the value of x+1xx + \frac{1}{x} is:

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  4. Question 4

    26 Jul 2023 S1

    54
    If x2−8x−1=0x^2 - 8x - 1 = 0, what is the value of x2+1x2x^2 + \frac{1}{x^2}?

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