A bilinear-linear bound on a weighted ellipsoid

Proved

WorkbookSource.plus_75322

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

lean-workbooksource-checked

Let $a,b,c$ be real numbers such that $a^2+2b^2+3c^2=36.$ Prove that $ab+bc+ca+a+20b+51c\leq 205$

Source: InternLM Lean-Workbook, record lean_workbook_plus_75322 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_75322 (a b c : ℝ) (h : a^2 + 2 * b^2 + 3 * c^2 = 36) : a * b + b * c + c * a + a + 20 * b + 51 * c ≤ 205   :=  by sorry

Source