lean_workbook_plus_42963

Proved

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

Let $a,b$ be positive reals. Show that $\frac{a}{b}+\frac{b}{a}+2\geq\frac{4(1+a^2)(1+b^2)}{(1+ab)^2}.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_42963 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) : (a / b + b / a + 2) ≥ 4 * (1 + a^2) * (1 + b^2) / (1 + a * b)^2   :=  by sorry

Source