Prove2Me

lean_workbook_plus_66130

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Let a,ba,b be reals. Prove that

a2+ab+b2≥3(a+b−1),a^2+ab+b^2\geq 3(a+b-1), a2+ab+b2≥3ab(a+b−ab),a^2+ab+b^2\geq 3ab(a+b-ab), a2+ab+b2≤3(a2−a+1)(b2−b+1).a^2+ab+b^2\leq 3(a^2-a+1)(b^2-b+1).
Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_66130 : ∀ a b : ℝ, a^2 + a * b + b^2 ≥ 3 * (a + b - 1) ∧ a^2 + a * b + b^2 ≥ 3 * a * b * (a + b - a * b) ∧ a^2 + a * b + b^2 ≤ 3 * (a^2 - a + 1) * (b^2 - b + 1)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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