A quartic bound formed from two squared linear factors

Proved

WorkbookSource.base_30799

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

lean-workbooksource-checked

Let $x,y,z \geq 0$ ,prove that: $2x^2(3x+y)^2+2y^2(3y+z)^2-(3x+y)^2y(2y+z+x)\geq 0$

Source: InternLM Lean-Workbook, record lean_workbook_30799 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_30799 (x y z : ℝ) : 2 * x ^ 2 * (3 * x + y) ^ 2 + 2 * y ^ 2 * (3 * y + z) ^ 2 - (3 * x + y) ^ 2 * y * (2 * y + z + x) ≥ 0  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_30799; Apache-2.0

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