lean_workbook_plus_72844

Proved

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

Prove the following inequality: $\frac{1}{(a+n)^{2}}+\frac{1}{(b+n)^{2}}\geq\frac{1}{ab+n^{2}}$ , where $a,b,n>1$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_72844 (a b n : ℝ) (ha : 1 < a) (hb : 1 < b) (hn : 1 < n) : (1 / (a + n) ^ 2 + 1 / (b + n) ^ 2) ≥ 1 / (a * b + n ^ 2)   :=  by sorry

Source

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

View graph