lean_workbook_plus_77251

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Let $a,b,c$ be real numbers. Prove that $3(a^2+b^2+c^2)^2+6(ab+bc+ca)^2\ge (a+b+c)^4$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_77251 (a b c : ℝ) : 3 * (a ^ 2 + b ^ 2 + c ^ 2) ^ 2 + 6 * (a * b + b * c + c * a) ^ 2 ≥ (a + b + c) ^ 4   :=  by sorry

Source