lean_workbook_plus_5538

Proved

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

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

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_5538 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) (habc : x * y * z = 1) : 1 / (1 + x + x^2) + 1 / (1 + y + y^2) + 1 / (1 + z + z^2) ≥ 1   :=  by sorry

Source

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

View graph