lean_workbook_plus_47982

Proved

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

For $x,\ y,\ z>0$ , such that $\sum \frac{1}{x^2+1}=2$ \nProve that : $xy+yz+zx\le \frac{3}{2}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_47982 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) (hx2 : x^2 + 1 > 0) (hy2 : y^2 + 1 > 0) (hz2 : z^2 + 1 > 0) (h : 1 / x^2 + 1 + 1 / y^2 + 1 + 1 / z^2 + 1 = 2) : x * y + y * z + z * x ≤ 3 / 2   :=  by sorry

Source

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

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