lean_workbook_plus_17986

Proved

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

By AM-GM \n\n

a^4+b^4+4a^2b^2 =\frac{(a^2+b^2)^2}{2}+\frac{(a^2+b^2)^2}{2}+2a^2b^2 \ge ab(a^2+b^2)+\frac{(a^2+b^2)^2}{2}+2a^2b^2 \ge 3ab(a^2+b^2 )

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_17986 : ∀ a b : ℝ, a^4 + b^4 + 4 * a^2 * b^2 ≥ 3 * a * b * (a^2 + b^2)   :=  by sorry

Source