lean_workbook_plus_3543

Proved

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

prove that $\frac{a}{\sqrt{1+bc}}+ \frac{b}{\sqrt{1+ac}}+ \frac{c}{\sqrt{1+ab}} \le \frac{3}{2}$ given $a,b,c>0$ and $a^2+b^2+c^2=1$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_3543 (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 / Real.sqrt (1 + b * c) + b / Real.sqrt (1 + a * c) + c / Real.sqrt (1 + a * b) ≤ 3 / 2   :=  by sorry

Source

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

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