A product of power sums bounded by an eighth-power sum

Proved

WorkbookSource.base_33810

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{(x^3+y^3+z^3)(x^5+y^5+z^5)}{x^8+y^8+z^8} \leq 3

Source: InternLM Lean-Workbook, record lean_workbook_33810 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_33810 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (x^3 + y^3 + z^3) * (x^5 + y^5 + z^5) / (x^8 + y^8 + z^8) ≤ 3  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_33810; Apache-2.0

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