lean_workbook_plus_31026

Proved

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

Let $a,b>0.$ Prove that $\frac{a^2}{b}+\frac{b^2}{2a+b}\geq \frac{a+b}{2}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_31026 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) : a^2 / b + b^2 / (2 * a + b) ≥ (a + b) / 2   :=  by sorry

Source