A quadratic bound in an open square

Proved

WorkbookSource.problem_31517

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

lean-workbooksource-checked

Prove that for $0<a,b<2$ , $a^2 + ab + b^2 < 3(a + b)$ .

Source: InternLM Lean-Workbook, record lean_workbook_31517 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble

import Mathlib
open Real

Formal statement

theorem WorkbookSource.problem_31517 (a b : ℝ) (h1 : 0 < a ∧ 0 < b) (h2 : a < 2 ∧ b < 2) : a^2 + a * b + b^2 < 3 * (a + b)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_31517; Apache-2.0

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