A cyclic squared reciprocal ratio lower bound

Proved

WorkbookSource.base_41664

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

lean-workbooksource-checked

Let $a,b,c >0$ . Prove that

\frac{b}{a^2} + \frac{c}{b^2} + \frac{a}{c^2} \geq \frac{9}{(a+b+c)}

Source: InternLM Lean-Workbook, record lean_workbook_41664 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_41664 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (b / a ^ 2 + c / b ^ 2 + a / c ^ 2) ≥ 9 / (a + b + c)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_41664; Apache-2.0

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