lean_workbook_plus_47985

Proved

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

Prove that $(ab+bc+ca)^2=\frac{1}{4}(a^2+b^2+c^2)^2$ given $a+b+c=0$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_47985 (a b c : ℝ) (h : a + b + c = 0) :
  (a * b + b * c + c * a) ^ 2 = (1 / 4) * (a ^ 2 + b ^ 2 + c ^ 2) ^ 2   :=  by sorry

Source

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

View graph