A shifted cyclic linear product ratio is at least two hundred forty-three

Proved

WorkbookSource.plus_77609

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

lean-workbooksource-checked

Let $x,y,z$ be positive real numbers. Prove that:

\frac{(2x+4y+3)(2y+4z+3)(2z+4x+3)}{xy+yz+zx} \ge 243

Source: InternLM Lean-Workbook, record lean_workbook_plus_77609 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_77609 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (2*x + 4*y + 3)*(2*y + 4*z + 3)*(2*z + 4*x + 3) / (x*y + y*z + z*x) ≥ 243   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_77609; Apache-2.0

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