lean_workbook_plus_38522

Proved

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

Prove that for all $x,y>0$ , \n

\sqrt{\frac{x^2+xy+y^2}{3}}\geq\frac{x+y}{2}

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_38522 (x y : ℝ) (hx : 0 < x) (hy : 0 < y) : √((x ^ 2 + x * y + y ^ 2) / 3) ≥ (x + y) / 2   :=  by sorry

Source