lean_workbook_plus_415

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove that for positive real numbers $x, y, z$ satisfying $xyz = 1$ , the following inequality holds:\n $(x^{2}+y^{2}+z^{2})(x^{4}+y^{4}+z^{4})\leq 3(x^{6}+y^{6}+z^{6})$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_415 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) (h : x * y * z = 1) : (x ^ 2 + y ^ 2 + z ^ 2) * (x ^ 4 + y ^ 4 + z ^ 4) ≤ 3 * (x ^ 6 + y ^ 6 + z ^ 6)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

View graph