lean_workbook_plus_74403

Proved

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

Let $a,b,c$ be positive real numbers. If $(a+b)(b+c)(c+a)=\sqrt{10}$ , then $(a^2+b^2)(b^2+c^2)(c^2+a^2)+12a^2b^2c^2\ge 3$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_74403 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) (h : (a + b) * (b + c) * (c + a) = Real.sqrt 10) :
  (a^2 + b^2) * (b^2 + c^2) * (c^2 + a^2) + 12 * a^2 * b^2 * c^2 ≥ 3   :=  by sorry

Source

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

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