lean_workbook_plus_21442

Proved

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

Prove that $(a+b+c)^2 \ge 3(ab+bc+ca)$ for $a,b,c>0$ and $abc=1$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_21442 (a b c : ℝ) (h : a > 0 ∧ b > 0 ∧ c > 0 ∧ a * b * c = 1) :
  (a + b + c) ^ 2 ≥ 3 * (a * b + b * c + c * a)   :=  by sorry

Source

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

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