Prove2Me

lean_workbook_plus_60532

Proved

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

Prove that for all real numbers x, y, and z, (x+y+z)2(xy+yz+zx)2≤3(x2+xy+y2)(y2+yz+z2)(z2+zx+x2)(x + y + z)^{2}(xy + yz + zx)^{2} \leq 3(x^{2} + xy + y^{2})(y^{2} + yz + z^{2})(z^{2} + zx + x^{2}).

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_60532 (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 + z*x + x ^ 2)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

View graph