lean_workbook_plus_78605

Disproved

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

prove that: \n $\frac{a^{2}}{2b+c}+\frac{b^{2}}{2c+a}+\frac{ c^{2}}{2a+b}\geq \frac{a^{2}+b^{2}+c^{2}}{a+b+c}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_78605 : ∀ a b c : ℝ, (a^2 / (2 * b + c) + b^2 / (2 * c + a) + c^2 / (2 * a + b) : ℝ) ≥ (a^2 + b^2 + c^2) / (a + b + c)   :=  by sorry

Source

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

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