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x = a + root b, y = a - root b: value of x^2 + y^2

The same question, asked 2 times: 18 Jan 2025 Tier II*, 20 Jan 2025 Tier II. Every wording below, oldest first.

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  1. Question 1

    18 Jan 2025 Tier II

    24
    If x=8+5x = 8 + \sqrt{5} and y=8−5y = 8 - \sqrt{5} then the value of x2+y2x^2 + y^2 is:

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  2. Question 2

    20 Jan 2025 Tier II

    28
    If x=4+6x = 4 + \sqrt{6} and y=4−6y = 4 - \sqrt{6} then the value of x2+y2x^2 + y^2 is:

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