A reciprocal fourth-power ratio with a cubic correction

Proved

WorkbookSource.base_50279

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

lean-workbooksource-checked

Prove that for all positive numbers $a,b,c$ then: $\frac {abc(a + b + c)}{a^{4} + b^{4} + c^{4}} + \frac {12(a^{3} + b^{3} + c^{3})}{(a + b + c)(a^{2} + b^{2} + c^{2})}\geq 5$

Source: InternLM Lean-Workbook, record lean_workbook_50279 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_50279 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a * b * c * (a + b + c) / (a ^ 4 + b ^ 4 + c ^ 4) + 12 * (a ^ 3 + b ^ 3 + c ^ 3) / ((a + b + c) * (a ^ 2 + b ^ 2 + c ^ 2))) ≥ 5  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_50279; Apache-2.0

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