A sixth-degree product inequality with coefficient twenty-seven

Proved

WorkbookSource.base_10852

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Prove the inequality $27(x^2+y^2)(y^2+z^2)(z^2+x^2) \ge 8xyz(x+y+z)^3$

Source: InternLM Lean-Workbook, record lean_workbook_10852 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_10852 (x y z : ℝ) : 27 * (x^2 + y^2) * (y^2 + z^2) * (z^2 + x^2) ≥ 8 * x * y * z * (x + y + z)^3  :=  by sorry

Source