A cyclic cubic ratio with a symmetric quadratic correction

Proved

WorkbookSource.base_12732

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Prove that for all positive reals $a,b,c$ : $\frac{a^2b+b^2c+c^2a}{a^3+b^3+c^3}+\frac{3(a^2+b^2+c^2)}{ab+bc+ca} \geq 4$

Source: InternLM Lean-Workbook, record lean_workbook_12732 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_12732 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 * b + b^2 * c + c^2 * a) / (a^3 + b^3 + c^3) + 3 * (a^2 + b^2 + c^2) / (a * b + b * c + c * a) ≥ 4  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_12732; Apache-2.0

View graph