A cyclic fifth-power ratio bounds the quadratic sum

Proved

WorkbookSource.base_28054

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+b^5}{bc^2} + \frac{b^5+c^5}{ca^2} + \frac{c^5+a^5}{ab^2}\geq2( a^2 + b^2 + c^2)

Source: InternLM Lean-Workbook, record lean_workbook_28054 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_28054 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^5 + b^5) / (b * c^2) + (b^5 + c^5) / (c * a^2) + (c^5 + a^5) / (a * b^2) ≥ 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_28054; Apache-2.0

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