A squared cyclic quadratic ratio sum bounds cubic ratios

Proved

WorkbookSource.base_39698

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

lean-workbooksource-checked

Let $a,b,c$ be positive numbers. Prove that:

$(\frac{a^{2}}{b}+\frac{b^{2}}{c}+\frac{c^{2}}{a})^{2}\ge 3(\frac{a^{3}}{b}+\frac{b^{3}}{c}+\frac{c^{3}}{a})$

Source: InternLM Lean-Workbook, record lean_workbook_39698 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_39698 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 / b + b^2 / c + c^2 / a)^2 ≥ 3 * (a^3 / b + b^3 / c + c^3 / a)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_39698; Apache-2.0

View graph