lean_workbook_plus_57076

Proved

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

Let $a,b,c$ are real numbers,prove that: $(a^2b+b^2c+c^2a)^2 \geq 3(a^2c+ab^2+bc^2)abc.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_57076 (a b c : ℝ) : (a^2 * b + b^2 * c + c^2 * a)^2 ≥ 3 * (a^2 * c + a * b^2 + b * c^2) * a * b * c   :=  by sorry

Source