A cyclic quadratic ratio sum bounds a normalized cubic sum

Proved

WorkbookSource.base_3587

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

lean-workbooksource-checked

The original arqady's inequality is: If $a, b, c>0$ prove that $\frac{a^2}{b+c}+\frac{b^2}{c+a}+\frac{c^2}{a+b}\ge\frac{3}{2}\cdot\frac{a^3+b^3+c^3}{a^2+b^2+c^2}$

Source: InternLM Lean-Workbook, record lean_workbook_3587 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_3587 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 / (b + c) + b^2 / (c + a) + c^2 / (a + b)) ≥ (3 / 2) * (a^3 + b^3 + c^3) / (a^2 + b^2 + c^2)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_3587; Apache-2.0

View graph