lean_workbook_plus_70149

Proved

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

For $x,y,z>0$ prove that: $\frac{x^2}{x^2+xy+y^2}+\frac{y^2}{y^2+yz+z^2}+\frac{z^2}{z^2+zx+x^2} \ge 1$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_70149 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (x^2 / (x^2 + x * y + y^2) + y^2 / (y^2 + y * z + z^2) + z^2 / (z^2 + z * x + x^2) ≥ 1)   :=  by sorry

Source

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

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