lean_workbook_plus_44451

Proved

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

Prove $(x+y+z)^{2}(xy+yz+zx)^{2} \le 3(x^{2}+xy+y^{2})(z^{2}+zx+x^{2})(y^{2}+yz+z^{2})$ given $x,y,z>0$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_44451 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (x + y + z) ^ 2 * (x * y + y * z + z * x) ^ 2 ≤ 3 * (x ^ 2 + x * y + y ^ 2) * (z ^ 2 + z * x + x ^ 2) * (y ^ 2 + y * z + z ^ 2)   :=  by sorry

Source

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

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