A squared cyclic ratio sum with a symmetric correction

Proved

WorkbookSource.base_23588

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

lean-workbooksource-checked

Let $a,b,c>0.$ Prove: $\frac{a^2}{b^2}+\frac{b^2}{c^2}+\frac{c^2}{a^2}+\frac{8(ab+ac+bc)}{a^2+b^2+c^2}\geq11$

Source: InternLM Lean-Workbook, record lean_workbook_23588 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_23588 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 / b^2 + b^2 / c^2 + c^2 / a^2 + 8 * (a * b + a * c + b * c) / (a^2 + b^2 + c^2)) ≥ 11  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_23588; Apache-2.0

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