A quadratic lower bound with mixed and linear terms

Proved

WorkbookSource.base_54998

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Prove that for any real numbers $a,b$ : $12 a^2+36 a b+36 b^2+7 \geq 18 a+24 b.$

Source: InternLM Lean-Workbook, record lean_workbook_54998 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_54998 (a b : ℝ) : 12 * a ^ 2 + 36 * a * b + 36 * b ^ 2 + 7 ≥ 18 * a + 24 * b  :=  by sorry

Source