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x + 1/x = k: find x - 1/x

The same question, asked 2 times: 17 Sep 2024 S3*, 19 Sep 2024 S2. Every wording below, oldest first.

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  1. Question 1

    17 Sep 2024 S3

    53
    If x is an integer such that x+1x=658x + \frac{1}{x} = \frac{65}{8}, then find the value of x−1xx - \frac{1}{x}.

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  2. Question 2

    19 Sep 2024 S2

    70
    If (x+1x)=7,x>0\left(x + \frac{1}{x}\right) = 7, x > 0. The positive value of (x−1x)\left(x - \frac{1}{x}\right) is:

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