lean_workbook_plus_44574

Proved

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

Let $a,b,c>0$ and $a^4+b^4+c\leq\frac {3}{2}$ . Prove that $abc + \frac {1}{abc}\geq\frac{5}{2}$ Equality holds when $a=b=\frac{1}{\sqrt 2},c=1.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_44574 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) (h : a ^ 4 + b ^ 4 + c ≤ 3 / 2) : a * b * c + 1 / (a * b * c) ≥ 5 / 2   :=  by sorry

Source

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

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