lean_workbook_plus_1295

Proved

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

Let $a,b,c\geq 0$ and $a^2+b^2+c^2+2abc=1.$ Prove that\n\n

(a+2b)^2 + (b+2c)^2 + (c+2a)^2 \leq 7

(a+b)^2 + (b+c)(c+a) \leq \frac{5}{2}

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_1295 (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 + 2 * b)^2 + (b + 2 * c)^2 + (c + 2 * a)^2 ≤ 7 ∧ (a + b)^2 + (b + c) * (c + a) ≤ 5 / 2   :=  by sorry

Source

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

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