lean_workbook_plus_14753

Proved

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

Let $a,b,c$ be nonegative real numbers such that $a^{2}+b^{2}+c^{2}=1,$ prove that $\frac a{\sqrt{1+bc}}+\frac b{\sqrt{1+ca}}+\frac c{\sqrt{1+ab}}\leq\frac32.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_14753 (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 + c * a) + c / Real.sqrt (1 + a * b) ≤ 3 / 2   :=  by sorry

Source

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

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