An affine product bound on an ellipse

Proved

WorkbookSource.base_16267

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

lean-workbooksource-checked

Prove that $xy - 2x + 5y\leq \frac{13}{4}$ given $5x^2 + 4xy + 11y^2 = 3$ .

Source: InternLM Lean-Workbook, record lean_workbook_16267 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_16267 (x y : ℝ) (h : 5 * x ^ 2 + 4 * x * y + 11 * y ^ 2 = 3) :
  x * y - 2 * x + 5 * y ≤ 13 / 4  :=  by sorry

Source