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Identity a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca)

This type of question, asked 3 times: 15 Nov 2020 Tier II, 29 Jan 2022 Tier II, 3 Feb 2022 Tier II. All 3 questions below, oldest first.

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  1. Question 1

    15 Nov 2020 Tier II

    31
    If a+b+c=6a + b + c = 6, a3+b3+c3−3abc=342a^3 + b^3 + c^3 - 3abc = 342, then what is the value of ab+bc+caab + bc + ca?

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  2. Question 2

    29 Jan 2022 Tier II

    61
    If a+b+c=1a + b + c = 1, ab+bc+ca=−22ab + bc + ca = -22 and abc=−40abc = -40, then what is the value of a3+b3+c3a^3 + b^3 + c^3?

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  3. Question 3

    3 Feb 2022 Tier II

    23
    If x=32.5x = 32.5, y=34.6y = 34.6 and z=30.9z = 30.9, then the value of x3+y3+z3−3xyzx^3 + y^3 + z^3 - 3xyz is 0.98k0.98k, where k is equal to:

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