lean_workbook_plus_79698

Proved

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

Prove that $x+y+xy/(\sqrt{x}+\sqrt{y})^2 \ge 9\sqrt{xy}/4$ for $x, y > 0$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_79698 (x y : ℝ) (hx : 0 < x) (hy : 0 < y) : x + y + x * y / (Real.sqrt x + Real.sqrt y) ^ 2 ≥ 9 * Real.sqrt (x * y) / 4   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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