Prove2Me

lean_workbook_plus_30196

Proved

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

Prove that (a2+b2+c2)(x2+y2+z2)+2(ab+bc+ca)(xy+yz+zx)≥0(a^2+b^2+c^2)(x^2+y^2+z^2)+2(ab+bc+ca)(xy+yz+zx)\ge 0 given x3+y3+z3=3xyzx^3+y^3+z^3=3xyz.

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_30196 (a b c x y z : ℝ) (h : x^3 + y^3 + z^3 = 3 * x * y * z) :
  (a^2 + b^2 + c^2) * (x^2 + y^2 + z^2) + 2 * (a * b + b * c + c * a) * (x * y + y * z + z * x) ≥ 0   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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