A weighted quadratic sum bounds a squared linear form

Proved

WorkbookSource.base_48622

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

lean-workbooksource-checked

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

a^2+ 2b^2+c^2+ab\geq \frac{7}{23}(a+2b+c)^2

Source: InternLM Lean-Workbook, record lean_workbook_48622 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_48622 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^2 + 2 * b^2 + c^2 + a * b ≥ (7 / 23) * (a + 2 * b + c)^2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_48622; Apache-2.0

View graph