lean_workbook_plus_15427

Proved

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

Let $a,\ b,\ c$ be real numbers such that $a+b+c=0$ . Prove that $a^2b^2+b^2c^2+c^2a^2+6abc\geq -3$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_15427 (a b c : ℝ) (hab : a + b + c = 0) : a ^ 2 * b ^ 2 + b ^ 2 * c ^ 2 + c ^ 2 * a ^ 2 + 6 * a * b * c ≥ -3   :=  by sorry

Source

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

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