lean_workbook_plus_16776

Proved

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

Prove that $xy/z^2 + y/x + x/y \geq 9/4$ for positive $x, y$ given $x+y=z$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_16776 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) (hxy : x + y = z) : x * y / z ^ 2 + y / x + x / y ≥ 9 / 4   :=  by sorry

Source

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

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