lean_workbook_plus_16664

Proved

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

Let $a$ , $b$ be real positive numbers such that $a\geq 2b$ Prove that $\frac{a^2}{b} + \frac{b^2}{a}$ $\geq$ $\frac{9a}{4}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_16664 (a b : ℝ) (hab : a ≥ 2 * b) (ha : a > 0) (hb : b > 0) : a^2 / b + b^2 / a ≥ 9 * a / 4   :=  by sorry

Source