A reciprocal sum and triple product inequality at fixed sum three

Proved

WorkbookSource.base_45572

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let $a,b,c>0$ and $a+b+c=3$ . Prove that: $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{48abc}{25}\ge\frac{123}{25}$

Source: InternLM Lean-Workbook, record lean_workbook_45572 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_45572 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) (habc : a + b + c = 3) : 1 / a + 1 / b + 1 / c + 48 * a * b * c / 25 ≥ 123 / 25  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_45572; Apache-2.0

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