lean_workbook_plus_2620

Proved

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

Note that $(a^2+2)(b^2+2) \ge 3\left[\frac{(a+b)^2}{2}+1\right] \Leftrightarrow 2(ab-1)^2+(a-b)^2 \ge 0$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_2620 (a b : ℝ) : (a^2 + 2) * (b^2 + 2) ≥ 3 * ((a + b)^2 / 2 + 1)   :=  by sorry

Source