lean_workbook_plus_48552

Proved

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

Prove that $\frac{1}{a^{2}}+\frac{1}{b}\ge \frac{4}{a^{2}+b}$ given $a,b,c >0$ and $abc=1$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_48552 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) : 1 / a ^ 2 + 1 / b ≥ 4 / (a ^ 2 + b)   :=  by sorry

Source

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

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