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x = a +/- sqrt(b) with conjugate reciprocal: find x +/- 1/x or x^2 + 1/x^2

This type of question, asked 2 times: 18 Sep 2024 S1, 20 Sep 2025 S1. All 2 questions below, oldest first.

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  1. Question 1

    18 Sep 2024 S1

    58
    If x=7−43x = 7 - 4\sqrt{3}, then find the value of (x2+1x2)\left(x^2 + \frac{1}{x^2}\right).

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  2. Question 2

    20 Sep 2025 S1

    71
    If x=2+3x = 2 + \sqrt{3}, find x−1xx - \frac{1}{x}.

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