lean_workbook_plus_289

Proved

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

Inequality follows from these three am-gm inequalities. \n $a^4b^2+b^4c^2 \geq 2b^3a^2c$ \n $a^4b^2+c^4a^2\geq 2a^3c^2b$ \n $b^4c^2+c^4a^2\geq 2c^3b^2a$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_289 (a b c : ℝ) :
  a^4 * b^2 + b^4 * c^2 ≥ 2 * b^3 * a^2 * c ∧
  a^4 * b^2 + c^4 * a^2 ≥ 2 * a^3 * c^2 * b ∧
  b^4 * c^2 + c^4 * a^2 ≥ 2 * c^3 * b^2 * a   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

View graph