lean_workbook_plus_5289

Proved

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

For $a,b,c>0$ prove that:\n $2+\frac{a^2+b^2+c^2}{ab+bc+ca}\ge\frac{a+b}{b+c}+\frac{b+c}{c+a}+\frac{c+a}{a+b}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_5289 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 2 + (a^2 + b^2 + c^2) / (a * b + b * c + c * a) ≥ (a + b) / (b + c) + (b + c) / (c + a) + (c + a) / (a + b)   :=  by sorry

Source

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

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