A cubed quadratic sum bounds three mixed quadratic factors

Proved

WorkbookSource.base_35771

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

lean-workbooksource-checked

Prove that $8(a^2+b^2+c^2)^3\geq27(a^2+bc)(b^2+ca)(c^2+ab)$ for all $a,b,c>0$ .

Source: InternLM Lean-Workbook, record lean_workbook_35771 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_35771 {a b c : ℝ} (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 8 * (a^2 + b^2 + c^2)^3 ≥ 27 * (a^2 + b * c) * (b^2 + c * a) * (c^2 + a * b)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_35771; Apache-2.0

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