lean_workbook_plus_17247

Proved

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

prove that, for positive reals $a$ , $b$ , and $c$ , $a^2+b^2+c^2\geq\frac{(a+b+c)^2}{3}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_17247 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^2 + b^2 + c^2 ≥ (a + b + c)^2 / 3   :=  by sorry

Source