lean_workbook_plus_79523

Proved

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

Let $a,b>0$ and $(a+\frac{1}{b})(b+\frac{1}{a})=5.$ Prove that

a+b\geq \sqrt5-1

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_79523 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) (hab : (a + 1/b) * (b + 1/a) = 5) : a + b ≥ Real.sqrt 5 - 1   :=  by sorry

Source