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Home » We want $ \mathbbE[\textoutput] $. - High Altitude Science

We want $ \mathbbE[\textoutput] $. - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Question: Let $ a, b, c $ be real numbers such that $ a + b + c = 0 $. Prove that $ a^3 + b^3 + c^3 = 3abc $.

📌 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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