lean_workbook_plus_4779

Disproved

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

Prove that $\frac {a^2(b + c)}{b^2 + c^2} + \frac {b^2(c + a)}{c^2 + a^2} + \frac {c^2(a + b)}{a^2 + b^2} \geq a + b + c$ using Chebyshev's and Nesbitt's inequalities.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_4779 : ∀ a b c : ℝ, (a^2 * (b + c) / (b^2 + c^2) + b^2 * (c + a) / (c^2 + a^2) + c^2 * (a + b) / (a^2 + b^2) ≥ a + b + c)   :=  by sorry

Source

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

View graph