A symmetric quadratic ratio with a refined triple-product correction

Proved

WorkbookSource.base_28828

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

The inequality is equivalent to $\frac{(x+y+z)^2}{xy+yz+zx}+\frac{32xyz}{(x+y+z)^3+5xyz}\ge 4$ for $x,y,z>0$ .

Source: InternLM Lean-Workbook, record lean_workbook_28828 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_28828 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (x + y + z) ^ 2 / (x * y + y * z + z * x) + 32 * x * y * z / ((x + y + z) ^ 3 + 5 * x * y * z) ≥ 4  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_28828; Apache-2.0

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