lean_workbook_plus_29947

Proved

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

If $a, b, c>0$ prove that \n $\frac{a(b+c)^2}{2a+b+c}+\frac{b(c+a)^2}{2b+c+a}+\frac{c(a+b)^2}{2c+a+b}\le ab+bc+ca$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_29947 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a * (b + c) ^ 2 / (2 * a + b + c) + b * (c + a) ^ 2 / (2 * b + c + a) + c * (a + b) ^ 2 / (2 * c + a + b) ≤ a * b + b * c + c * a)   :=  by sorry

Source

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

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