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Sum of squares equals zero: each term zero, then evaluate

This type of question, asked 2 times: 18 Jul 2023 S3, 12 Sep 2024 S3. All 2 questions below, oldest first.

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  1. Question 1

    18 Jul 2023 S3

    51
    If a2+b2+c2=ab+bc+aca^2 + b^2 + c^2 = ab + bc + ac, then the value of 11a4+13b4+17c417a2b2+9b2c2+15c2a2\frac{11 a^4 + 13 b^4 + 17 c^4}{17 a^2b^2 + 9b^2c^2 + 15 c^2a^2} is:

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  2. Question 2

    12 Sep 2024 S3

    62
    If a2+b2+c2=2(a+c−1)a^2 + b^2 + c^2 = 2(a + c - 1), then the value of a3+b3+c3=a^3 + b^3 + c^3 =?

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