lean_workbook_plus_1552

Proved

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

If $a,b,c>0$ and $a^2+b^2+c^2+2abc=1$ , prove that $(a+b)^2 + (b+c)^2 + (c+a)^2 \leq 3.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_1552 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) (h : a^2 + b^2 + c^2 + 2 * a * b * c = 1) : (a + b)^2 + (b + c)^2 + (c + a)^2 ≤ 3   :=  by sorry

Source

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

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