lean_workbook_plus_11101

Proved

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

Let $a,b,c >0$ with $a^2+b^2+c^2=1$ . Prove that: $\frac{a}{1-a^2}+\frac{b}{1-b^2}+\frac{c}{1-c^2} \ge \frac{3 \sqrt{3}}{2}$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_11101 (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 / (1 - a^2) + b / (1 - b^2) + c / (1 - c^2) ≥ (3 * Real.sqrt 3) / 2   :=  by sorry

Source

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

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