lean_workbook_plus_26277

Proved

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

Let $a,b,c\in \mathbb{R}$ such that $a^3b+b^3c+c^3a=0$ . Show that:\n\n $a^4+b^4+c^4+2abc(a+b+c)\ge 0$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_26277 (a b c : ℝ) (h : a ^ 3 * b + b ^ 3 * c + c ^ 3 * a = 0) :
  a ^ 4 + b ^ 4 + c ^ 4 + 2 * a * b * c * (a + b + c) ≥ 0   :=  by sorry

Source

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

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