A bilinear upper bound under a quadratic constraint

Proved

WorkbookSource.base_46854

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

lean-workbooksource-checked

Let $a$ and $b$ be real numbers such that $9a^2+8ab+7b^2\leq6$ . Prove that $7a+5b+12ab\leq9$ .

Source: InternLM Lean-Workbook, record lean_workbook_46854 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_46854 (a b : ℝ) (h : 9 * a ^ 2 + 8 * a * b + 7 * b ^ 2 ≤ 6) :
 7 * a + 5 * b + 12 * a * b ≤ 9  :=  by sorry

Source