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Home » Let \( x, y, z \) be positive real numbers. Find the minimum value of - go-checkin.com

Let \( x, y, z \) be positive real numbers. Find the minimum value of - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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x \in (-\infty, 2) \cup \left(rac{11}{3}, \infty
oxed{(-\infty, 2) \cup \left(rac{11}{3}, \infty
Question: Let $ a, b, c $ be real numbers such that $ a + b + c = 0 $....
Solution: We use the well-known algebraic identity:
a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca).
Given that $ a + b + c = 0 $, substitute into the identity:
a^3 + b^3 + c^3 - 3abc = 0 \cdot (a^2 + b^2 + c^2 - ab - bc - ca) = 0.
a^3 + b^3 + c^3 = 3abc.
This completes the proof.
oxed{a^3 + b^3 + c^3 = 3abc}

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