lean_workbook_plus_8657

Proved

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

Let $a,b,c$ be positive reals, show that \n $a^3b^2 + b^3c^2 + c^3a^2 \geq a^2b^2c + b^2c^2a + c^2a^2b$ . \n

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_8657 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^3 * b^2 + b^3 * c^2 + c^3 * a^2 ≥ a^2 * b^2 * c + b^2 * c^2 * a + c^2 * a^2 * b   :=  by sorry

Source

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

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