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Use x^3 + y^3 + z^3 - 3xyz = (x + y + z)(x^2 + y^2 + z^2 - xy - yz - zx)

This type of question, asked 2 times: CDS 2 2023, CDS 1 2025. All 2 questions below, oldest first.

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  1. Question 1

    CDS 2 2023

    1
    If a2−bc=αa^2 - bc = \alpha, b2−ac=βb^2 - ac = \beta, c2−ab=γc^2 - ab = \gamma, then what is aα+bβ+cγ(a+b+c)(α+β+γ)\dfrac{a\alpha + b\beta + c\gamma}{(a + b + c)(\alpha + \beta + \gamma)} equal to ?

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  2. Question 2

    CDS 1 2025

    40
    If x, y, z are real numbers such that x+y+z=10x + y + z = 10 and xy+yz+zx=18xy + yz + zx = 18, then what is the value of x3+y3+z3−3xyzx^3 + y^3 + z^3 - 3xyz ?

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