lean_workbook_plus_47791

Proved

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

if a,b,c>o, prove that $a^3/(b+c) + b^3/(a+c) + c^3/(a+b)\geq(a^2+b^2+c^2)/2$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_47791 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^3 / (b + c) + b^3 / (a + c) + c^3 / (a + b) ≥ (a^2 + b^2 + c^2) / 2   :=  by sorry

Source

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

View graph