lean_workbook_plus_9284

Proved

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

Let $a,b,c$ be positive real numbers such that $a\sqrt{a}+b\sqrt{b}+c\sqrt{c} \ge3$ then prove that;\n\n

abc+2 \ge \frac{9}{a^3+b^3+c^3}

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_9284 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) : a * Real.sqrt a + b * Real.sqrt b + c * Real.sqrt c >= 3 → a * b * c + 2 >= 9 / (a ^ 3 + b ^ 3 + c ^ 3)   :=  by sorry

Source

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

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