lean_workbook_plus_60864

Proved

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

Let a,b,c be real numbers such that $a+b+c=0$ . Prove that $\ (|a|+|b|+|c|)^2\geqq 2(a^2+b^2+c^2).$ When does equality holds?

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_60864 (a b c : ℝ) (h : a + b + c = 0) :
  (|a| + |b| + |c|) ^ 2 ≥ 2 * (a ^ 2 + b ^ 2 + c ^ 2)   :=  by sorry

Source