lean_workbook_plus_59498

Proved

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

Corrected inequality: $(x+y+z)^{2}(xy+yz+zx)^{2}\leq 3(x^{2}+xy+y^{2})(y^{2}+yz+z^{2})(z^{2}+xz+x^{2})$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_59498 (x y z : ℝ) :
  (x + y + z) ^ 2 * (x * y + y * z + z * x) ^ 2 ≤
    3 * (x ^ 2 + x * y + y ^ 2) * (y ^ 2 + y * z + z ^ 2) * (z ^ 2 + x * z + x ^ 2)   :=  by sorry

Source

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

View graph