lean_workbook_plus_75836

Proved

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

Let $a,b,c$ be real numbers such that $a^2(b+c)+b^2(a+c)+c^2(a+b)=0$ . Prove that $ab+bc+ca\leq0$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_75836 (a b c : ℝ) (h : a^2 * (b + c) + b^2 * (a + c) + c^2 * (a + b) = 0) : a * b + b * c + c * a ≤ 0   :=  by sorry

Source