lean_workbook_plus_49777

Proved

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

Prove that $\frac{3(a^2+b^2+c^2)}{2(ab+bc+ca)}\ge \frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b}$ for positive real numbers $a, b, c$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_49777 : ∀ a b c : ℝ, a > 0 ∧ b > 0 ∧ c > 0 → 3 * (a ^ 2 + b ^ 2 + c ^ 2) / (2 * (a * b + b * c + c * a)) ≥ a / (b + c) + b / (c + a) + c / (a + b)   :=  by sorry

Source

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

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