lean_workbook_plus_5983

Proved

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

If $a,b,c>0$ prove that:\n $2\sqrt{(a^2b+b^2c+c^2a)(a+b+c)}\ge 2(ab+bc+ca)$ \n\n__________\n\nMarin Sandu

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_5983 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 2 * Real.sqrt ((a^2 * b + b^2 * c + c^2 * a) * (a + b + c)) ≥ 2 * (a * b + b * c + c * a)   :=  by sorry

Source

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

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