lean_workbook_plus_60186

Proved

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

Let $x,y>0$ .Prove that \n

\frac{y}{x}+\frac{x}{y}+\frac{xy}{ (x+y)^2}\ge{\frac{9}{4}}

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_60186 (x y : ℝ) (hx : 0 < x) (hy : 0 < y) : (y / x + x / y + (x * y) / (x + y) ^ 2) ≥ 9 / 4   :=  by sorry

Source