lean_workbook_plus_12634

Proved

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

Prove that for positive numbers $a, b, c$ with $a^2 + b^2 + c^2 = 1$ , the following inequality also holds: $\frac{a+b}{3+5ab} + \frac{b+c}{3+5bc} + \frac{c+a}{3+5ca} \leq \frac{3\sqrt{3}}{7}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_12634 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) (hab : a + b + c = 1) : (a + b) / (3 + 5 * a * b) + (b + c) / (3 + 5 * b * c) + (c + a) / (3 + 5 * c * a) ≤ (3 * Real.sqrt 3) / 7   :=  by sorry

Source

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

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