lean_workbook_plus_775

Proved

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

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

\frac{b + c}{a}+\frac{c + a}{b}+\frac{a + b} {c}\ge 2+ \frac {4(a^2+b^2+c^2)}{ab+bc+ca}

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_775 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (b + c) / a + (c + a) / b + (a + b) / c ≥ 2 + (4 * (a ^ 2 + b ^ 2 + c ^ 2)) / (a * b + b * c + a * c)   :=  by sorry

Source

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

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