Prove2Me

lean_workbook_plus_79898

Proved

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

prove that a2(b+c−a)+b2(a+c−b)+c2(a+b−c)≤3abc a^2(b+c-a)+b^2(a+c-b)+c^2(a+b-c)\le{3abc}\n\na,b,c - triangle side lengths.

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_79898 (a b c : ℝ) (hx: a > 0 ∧ b > 0 ∧ c > 0) (hab : a + b > c) (hbc : b + c > a) (hca : a + c > b) : a^2 * (b + c - a) + b^2 * (a + c - b) + c^2 * (a + b - c) ≤ 3 * a * b * c   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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