lean_workbook_plus_8296

Proved

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

Let $a,b,c>0$ and $a^2+b^2+c^2=1$ prove that \n $a+b+c+\frac{1}{abc}\ge \frac{4\sqrt{3}}{9}(a+b+c)(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_8296 (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 = 1) : a + b + c + 1 / (a * b * c) ≥ (4 * Real.sqrt 3 / 9) * (a + b + c) * (1 / a + 1 / b + 1 / c)   :=  by sorry

Source

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

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