lean_workbook_plus_51147

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Given $a(bc-a^2) + b(ca-b^2) + c(ab-c^2) = 0$ , prove that $a^3+b^3+c^3-3abc=0$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_51147 (a b c : ℝ) (h : a * (b * c - a ^ 2) + b * (c * a - b ^ 2) + c * (a * b - c ^ 2) = 0) : a ^ 3 + b ^ 3 + c ^ 3 - 3 * a * b * c = 0   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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