lean_workbook_plus_12121

Proved

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

Let $a, b, c$ be real positive numbers such that $a^2+b^2+c^2=3.$ Prove that

ab+bc+ca \le abc+2.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_12121 (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 = 3) : a * b + b * c + c * a ≤ a * b * c + 2   :=  by sorry

Source

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

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