lean_workbook_plus_64337

Proved

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

Let $a,b,c$ be positive real numbers. Prove that $a^5c^2+b^5a^2+c^5b^2\geq abc(a^3c+b^3a+c^3b)$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_64337 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^5 * c^2 + b^5 * a^2 + c^5 * b^2 ≥ a * b * c * (a^3 * c + b^3 * a + c^3 * b)   :=  by sorry

Source

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

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