lean_workbook_plus_9397

Proved

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

Let $a,b,c$ are real numbers,prove that: $(a^3+b^3+c^3)(a+b+c)\geq (ab+bc+ac)(a^2+b^2+c^2).$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_9397 (a b c : ℝ) : (a ^ 3 + b ^ 3 + c ^ 3) * (a + b + c) ≥ (a * b + b * c + a * c) * (a ^ 2 + b ^ 2 + c ^ 2)   :=  by sorry

Source

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

View graph