lean_workbook_plus_15018

Proved

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

Hence \n $\frac1{\sqrt{a}+\sqrt{(a+b)(a+c)}} \le \frac19\left(\frac1{\sqrt{a}}+\frac4{\sqrt{(a+b)(a+c)}}\right)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_15018 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 1 / (√a + √((a + b) * (a + c))) ≤ 1 / 9 * (1 / √a + 4 / √((a + b) * (a + c)))   :=  by sorry

Source

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

View graph