lean_workbook_plus_19119

Proved

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

Let $a,b,c$ be positive real numbers such that $a^3+b^3+c^3+abc=4$ . Prove that:\n

\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}+3abc\geq 6

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_19119 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) (h : a ^ 3 + b ^ 3 + c ^ 3 + a * b * c = 4) : 1 / a ^ 2 + 1 / b ^ 2 + 1 / c ^ 2 + 3 * a * b * c ≥ 6   :=  by sorry

Source

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

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