A squared quadratic sum with a triple-product correction

Proved

WorkbookSource.plus_43984

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

lean-workbooksource-checked

Let $a$ , $b$ and $c$ be real numbers such that $a+b+c=3$ . Prove that:

(a^2+b^2+c^2)^2+3abc\geq4(a^2+b^2+c^2)

Source: InternLM Lean-Workbook, record lean_workbook_plus_43984 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_43984 (a b c : ℝ) (h : a + b + c = 3) : (a^2 + b^2 + c^2)^2 + 3 * a * b * c ≥ 4 * (a^2 + b^2 + c^2)   :=  by sorry

Source