An asymmetric mixed ratio sum is at least five halves

Proved

WorkbookSource.base_42334

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

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

\frac{2a}{b+c}+\frac{b^2}{c^2+a^2}+\frac{2c}{a+b} \geq \frac{5}{2}

Source: InternLM Lean-Workbook, record lean_workbook_42334 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_42334 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (2 * a / (b + c) + b^2 / (c^2 + a^2) + 2 * c / (a + b)) ≥ 5 / 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_42334; Apache-2.0

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