A parameterized quadratic inequality in three variables

Proved

WorkbookSource.base_51926

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+b^2+c^2+ka+\frac{k^2}{3}\ge ab+bc+ca+kc

Where $k\in R.$

Source: InternLM Lean-Workbook, record lean_workbook_51926 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_51926 (a b c k : ℝ): a^2 + b^2 + c^2 + k*a + k^2 / 3 ≥ a * b + b * c + c * a + k * c  :=  by sorry

Source