lean_workbook_plus_33845

Proved

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

$(a+b+c)(a^2+b^2+c^2)\geq 9abc= 9(4R\triangle)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_33845 {a b c : ℝ} (hx: a > 0 ∧ b > 0 ∧ c > 0) (hab : a + b > c) (hbc : b + c > a) (hca : a + c > b) : (a+b+c)*(a^2+b^2+c^2) ≥ 9*a*b*c   :=  by sorry

Source

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

View graph