lean_workbook_plus_11592

Proved

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

Prove for all positive real x, y and z, that $(xy+yz+zx)^{3}\le 27((x+y)(y+z)(z+x))^2$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_11592 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (x * y + y * z + z * x)^3 ≤ 27 * ((x + y) * (y + z) * (z + x))^2   :=  by sorry

Source

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

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