Prove2Me

lean_workbook_plus_31937

Disproved

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

Prove the following inequality: a2+3bc(b+c)2+b2+3ca(c+a)2+c2+3ab(a+b)2≥114+2abc(a+b)(b+c)(c+a)\frac{a^2+3bc}{(b+c)^2}+\frac{b^2+3ca}{(c+a)^2}+\frac{c^2+3ab}{(a+b)^2} \ge \frac{11}{4}+\frac{2abc}{(a+b)(b+c)(c+a)}

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_31937 : ∀ a b c : ℝ, (a^2 + 3 * b * c) / (b + c)^2 + (b^2 + 3 * c * a) / (c + a)^2 + (c^2 + 3 * a * b) / (a + b)^2 ≥ 11 / 4 + 2 * a * b * c / (a + b) / (b + c) / (c + a)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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