A linear term and shifted square bound a harmonic product

Proved

WorkbookSource.base_55508

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let $a,b$ be positive real numbers .Prove that

a+(b+1)^2\geq \frac{9ab}{a+b}

(Lijvzhi)

Source: InternLM Lean-Workbook, record lean_workbook_55508 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_55508 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) : a + (b + 1) ^ 2 ≥ 9 * a * b / (a + b)  :=  by sorry

Source