A bound on a quadratic locus involving square root of three

Proved

WorkbookSource.base_908

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

lean-workbooksource-checked

If $x^2+y^2+xy+\sqrt{3}(x+y)=0$ , prove that $x^2+y^2\leq3$

Source: InternLM Lean-Workbook, record lean_workbook_908 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_908 (x y : ℝ) (h : x^2 + y^2 + x * y + Real.sqrt 3 * (x + y) = 0) :
  x^2 + y^2 ≤ 3  :=  by sorry

Source