A total and squared pair-product ratio sum is at least twenty ninths

Proved

WorkbookSource.plus_41300

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

lean-workbooksource-checked

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

a+b+c+\frac{(ab+bc+ca-2)^2}{a+b+c}\ge\frac{20}{9}

Source: InternLM Lean-Workbook, record lean_workbook_plus_41300 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_41300 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a + b + c + (a * b + b * c + c * a - 2) ^ 2 / (a + b + c) ≥ 20 / 9   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_41300; Apache-2.0

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