Prove2Me

A weighted pairwise quadratic sum has a squared lower bound

Proved
WorkbookSource.base_10100

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

lean-workbooksource-checked

Let a,b,c>0a,b,c>0 ,prove: (3(a+b)2+2(a+c)2+(b+c)2)2abc(a+b+c)≥176\frac{\left(3 (a+b)^2+2 (a+c)^2+(b+c)^2\right)^2}{a b c (a+b+c)}\geq 176 .

Source: InternLM Lean-Workbook, record lean_workbook_10100 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_10100 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (3 * (a + b) ^ 2 + 2 * (a + c) ^ 2 + (b + c) ^ 2) ^ 2 / (a * b * c * (a + b + c)) ≥ 176  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_10100; Apache-2.0

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