Prove2Me

lean_workbook_plus_48763

Proved

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

Let a,b,c>0.a,b,c>0 . Prove that \n

3(a2+b2+c2)2(ab+bc+ca)≥ab+c+ba+c+cb+a\frac{3(a^2+b^2+c^2)}{2(ab+bc+ca)} \geq \frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{b+a}
Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_48763 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) :  3 * (a ^ 2 + b ^ 2 + c ^ 2) / (2 * (a * b + b * c + c * a)) ≥ a / (b + c) + b / (a + c) + c / (b + a)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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