lean_workbook_plus_17109

Proved

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

Let $x,y,z>0,xyz=1$ . Prove that $\dfrac{1}{x^2+x+1}+\dfrac{1}{y^2+y+1}+\dfrac{1}{z^2+z+1}\geq 1$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_17109 (x y z : ℝ) (hx : x > 0) (hy : y > 0) (hz : z > 0) (habc : 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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