A quadratic form with a nonnegative parameter

Proved

WorkbookSource.base_12152

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

lean-workbooksource-checked

Let $a,b,c$ be real numbers. Prove that

a^2+2b^2+2c^2+ka+\frac{7k^2}{24}\ge ab+2bc+ca+kc

Where $k\geq 0.$

Source: InternLM Lean-Workbook, record lean_workbook_12152 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_12152 (a b c k : ℝ) (h : k ≥ 0) : a^2 + 2 * b^2 + 2 * c^2 + k * a + 7 * k^2 / 24 ≥ a * b + 2 * b * c + c * a + k * c  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_12152; Apache-2.0

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