lean_workbook_plus_52670

Proved

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

Prove the inequality: $a^2(a-(b+c))^2+a^2(b^2+c^2)+(b^2+c^2)(b-c)^2\ge 2a(b+c)(b-c)^2$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_52670 (a b c : ℝ) : a^2 * (a - (b + c))^2 + a^2 * (b^2 + c^2) + (b^2 + c^2) * (b - c)^2 ≥ 2 * a * (b + c) * (b - c)^2   :=  by sorry

Source

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

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