A rational inequality involving cubic and pairwise sums

Proved

WorkbookSource.base_5503

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

lean-workbooksource-checked

Strengthening : Let $a,b,c$ be positive real numbers.Prove that ${ \frac{a^3+b^3+c^3}{abc}+24 \geq \frac{8(a+b+c)^3}{(b+c)(c+a)(a+b)}}$

Source: InternLM Lean-Workbook, record lean_workbook_5503 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_5503 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^3 + b^3 + c^3) / (a * b * c) + 24 ≥ (8 * (a + b + c)^3) / ((b + c) * (c + a) * (a + b))  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_5503; Apache-2.0

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