A quadratic-product upper bound at fixed positive sum

Proved

WorkbookSource.base_31850

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

lean-workbooksource-checked

If $a,b,c > 0$ such that $a+b+c=3$ Prove that $3(a^{2}+b^{2}+c^{2})+abc\leq 27$

Source: InternLM Lean-Workbook, record lean_workbook_31850 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_31850 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 3) : 3 * (a ^ 2 + b ^ 2 + c ^ 2) + a * b * c ≤ 27  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_31850; Apache-2.0

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