A quadratic lower bound on a hyperbola

Proved

WorkbookSource.base_28896

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

lean-workbooksource-checked

Let $x,y$ be reals such that $5x^2- 4xy-y^2=5.$ Prove that $2x^2+y^2\geq \frac{5}{3}$

Source: InternLM Lean-Workbook, record lean_workbook_28896 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_28896  (x y : ℝ)
  (h₀ : 5 * x^2 - 4 * x * y - y^2 = 5) :
  2 * x^2 + y^2 ≥ 5 / 3  :=  by sorry

Source