lean_workbook_plus_9482

Proved

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

If $x,y,z>0$ show that:\n $\frac{(y+z)(z+x)(x+y)}{4xyz}\ge 1+\frac{x^2+y^2+z^2}{xy+yz+zx}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_9482 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (y + z) * (z + x) * (x + y) / (4 * x * y * z) ≥ 1 + (x ^ 2 + y ^ 2 + z ^ 2) / (x * y + y * z + z * x)   :=  by sorry

Source

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

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