lean_workbook_plus_51211

Proved

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

Now apply QM-AM: $\sqrt{\frac{y^2+x^2+x^2}{3}}\geq\frac{y+x+x}{3}\Rightarrow \sqrt{2x^2+y^2}\geq\frac{2x+y}{\sqrt{3}}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_51211  (x y : ℝ) :
  Real.sqrt (2 * x^2 + y^2) ≥ (2 * x + y) / Real.sqrt 3   :=  by sorry

Source