A squared cubic sum bounds a fourth-power triple product

Proved

WorkbookSource.base_48908

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

lean-workbooksource-checked

The following inequalities are also true. Let $a$ , $b$ and $c$ are non-negative numbers. Prove that: $(a+b+c)(a^3+b^3+c^3)^2\geq9abc(a^4+b^4+c^4)$

Source: InternLM Lean-Workbook, record lean_workbook_48908 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_48908 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) : (a + b + c) * (a ^ 3 + b ^ 3 + c ^ 3) ^ 2 ≥ 9 * a * b * c * (a ^ 4 + b ^ 4 + c ^ 4)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_48908; Apache-2.0

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