lean_workbook_plus_13191

Proved

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

Let $a,b,c\ge 0$ and $a^3+2b^3+2c^3=a+2b+2c$ . Prove that \n

a^2+2b^2+2c^2\leq 5

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_13191 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) (ha3 : a^3 + 2 * b^3 + 2 * c^3 = a + 2 * b + 2 * c) : a^2 + 2 * b^2 + 2 * c^2 ≤ 5   :=  by sorry

Source

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

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