A pairwise-product bound under two quadratic equalities

Proved

WorkbookSource.base_24507

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

lean-workbooksource-checked

Let $a,b,c$ satisfy $a^2+ab+b^2=3$ and $b^2+bc+c^2=16$ . Prove that $ab+bc+ca\le 8$ .

Source: InternLM Lean-Workbook, record lean_workbook_24507 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_24507 (a b c : ℝ) (ha : a^2 + a * b + b^2 = 3) (hb : b^2 + b * c + c^2 = 16) : a * b + b * c + c * a ≤ 8  :=  by sorry

Source