lean_workbook_plus_59702

Proved

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

If $a,b,c >0$ and $a^2+b^2+c^2=1$ , prove that: $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+a+b+c \ge 4 \sqrt{3}$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_59702 (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) : 1 / a + 1 / b + 1 / c + a + b + c ≥ 4 * Real.sqrt 3   :=  by sorry

Source

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

View graph