A twelfth-power sum with a pair-product correction at fixed total three

Proved

WorkbookSource.base_33327

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

lean-workbooksource-checked

Prove that $a^{12}+b^{12}+c^{12}+8(ab+bc+ca) \geq 27$ for real positive numbers $a, b, c$ with $a+b+c=3$ .

Source: InternLM Lean-Workbook, record lean_workbook_33327 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_33327 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b + c = 3) : a ^ 12 + b ^ 12 + c ^ 12 + 8 * (a * b + b * c + c * a) ≥ 27  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_33327; Apache-2.0

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