lean_workbook_plus_1299

Proved

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

Let $x,y$ be positive real numbers satisfying $\frac {1}{x(x+3y)}+ \frac {1}{y(y+3x)}= 1$ . Prove that $xy\le \frac {1}{2}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_1299 (x y : ℝ) (hx : 0 < x) (hy : 0 < y) : (1 / (x * (x + 3 * y)) + 1 / (y * (y + 3 * x)) = 1 → x * y ≤ 1 / 2)   :=  by sorry

Source

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

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