lean_workbook_plus_46804

Proved

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

Show that for positive real numbers $a, b, c$ ,\n $8a^3+3b^3+3c^3+b^2c+bc^2\geqslant 4(a^2b+ab^2+a^2c+ac^2).$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_46804 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 8 * a ^ 3 + 3 * b ^ 3 + 3 * c ^ 3 + b ^ 2 * c + b * c ^ 2 ≥ 4 * (a ^ 2 * b + a * b ^ 2 + a ^ 2 * c + a * c ^ 2)   :=  by sorry

Source

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

View graph