A cyclic fifth-power ratio sum bounds the quadratic sum

Proved

WorkbookSource.plus_45396

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

lean-workbooksource-checked

Let $a, b, c$ be positive reals. Show that $\frac{a^5}{bc^2} + \frac{b^5}{ca^2} + \frac{c^5}{ab^2} \ge a^2 + b^2 + c^2.$

Source: InternLM Lean-Workbook, record lean_workbook_plus_45396 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_45396 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^5 / b / c^2 + b^5 / c / a^2 + c^5 / a / b^2 ≥ a^2 + b^2 + c^2   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_45396; Apache-2.0

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