lean_workbook_plus_19951

Proved

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

Using the Arithmetic Mean-Geometric Mean inequality, $\left(\frac{(a^2+b^2+c^2)}{3}\right)^3 \geq \frac{27}{8}(a^2+b^2)(b^2+c^2)(c^2+a^2)$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_19951 (a b c : ℝ) :
  (3 * (a^2 + b^2 + c^2) / 3)^3 ≥ (27 / 8) * (a^2 + b^2) * (b^2 + c^2) * (c^2 + a^2)   :=  by sorry

Source