lean_workbook_plus_3120

Proved

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

we know $2bc\leq{b^2+c^2}$ , $2ca\leq{c^2+a^2}$ , and $2ab\leq{a^2+b^2}$ ,\nby adding these and add $4(bc+ca+ab)$ both sides ,you get\n $3(bc+ca+ab)\leq(a+b+c)^{2}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_3120 (a b c : ℝ) : 3 * (b * c + c * a + a * b) ≤ (a + b + c) ^ 2   :=  by sorry

Source

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

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