A pair-product sum bounds a squared triple-product expression

Proved

WorkbookSource.plus_14336

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

lean-workbooksource-checked

Let $x,y,z>0$ and $x+y+z=3$ . Prove the inequality: $\frac{64}{3}(xy+yz+xz)\le55+9(xyz)^2$ .

Source: InternLM Lean-Workbook, record lean_workbook_plus_14336 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_14336 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) (h : x + y + z = 3) : (64 / 3) * (x * y + y * z + z * x) ≤ 55 + 9 * (x * y * z) ^ 2   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_14336; Apache-2.0

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