A pairwise-product maximum under a quadratic relation

Proved

WorkbookCorrected.base_46350

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

corrected-formalizationlean-workbooksource-checked

Let $a,b,c\in \mathbb{R}$ and $a^{2}+b^{2}+c^{2}+4ab=128$ . Find maximum of $ab+bc+ac$

Source: InternLM Lean-Workbook, record lean_workbook_46350 (Apache-2.0). Natural-language proposition preserved; the source bound is completed with an exact attainment witness. Proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookCorrected.base_46350 : (∀ (a b c : ℝ) (h : a^2 + b^2 + c^2 + 4 * a * b = 128), a * b + b * c + c * a ≤ 64) ∧ (∃ a b c : ℝ, (a^2 + b^2 + c^2 + 4 * a * b = 128) ∧ (
  a * b + b * c + c * a  =  64  )) := by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_46350; Apache-2.0

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