lean_workbook_plus_11847

Proved

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

Given $a, b, c$ positive numbers, $a^2 + b^2 + c^2 = 3$ . Prove that: $2(a + b + c) + \frac{1}{abc} \geq 7$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_11847 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) (hab : a + b + c = 3) : 2 * (a + b + c) + 1 / (a * b * c) ≥ 7   :=  by sorry

Source

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

View graph