A cyclic quadratic ratio bounds a symmetric cubic ratio

Proved

WorkbookSource.base_31287

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

lean-workbooksource-checked

Let $a,b,c \in R^{+}$ .Prove that $\frac{a^2}{b} + \frac{b^2}{c} + \frac{c^2}{a} + a+b+c \ge \frac{2(a+b+c)^3}{3(ab+bc+ca)}$ .

Source: InternLM Lean-Workbook, record lean_workbook_31287 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_31287 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^2 / b + b^2 / c + c^2 / a + a + b + c ≥ 2 * (a + b + c)^3 / (3 * (a * b + b * c + c * a))  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_31287; Apache-2.0

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