lean_workbook_plus_25990

Proved

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

Let $a,y,z>0$ and xyz=1. Prove that $\frac{1}{x^2+x+1}+\frac{1}{y^2+y+1}+\frac{1}{z^2+z+1}\geq1$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_25990 (x y z : ℝ) (hx : x > 0) (hy : y > 0) (hz : z > 0) (h : x * y * z = 1) : 1 / (x^2 + x + 1) + 1 / (y^2 + y + 1) + 1 / (z^2 + z + 1) >= 1   :=  by sorry

Source

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

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