lean_workbook_plus_20239

Proved

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

Let $a,b,c$ be positive real numbers such that $a+b+c=1$ . Prove that $\frac {1} {a} +\frac {1} {b} +\frac{1} {c} \geq \frac { 25} { 1+48abc}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_20239 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) : 1 / a + 1 / b + 1 / c ≥ 25 / (1 + 48 * a * b * c)   :=  by sorry

Source

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

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