lean_workbook_plus_29447

Proved

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

Prove that $x + \frac{1}{x^2} \geq 2$ for $x \in (0, 1]$ using the Arithmetic Mean-Geometric Mean (AM-GM) inequality.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_29447 (x : ℝ) (hx : 0 < x ∧ x ≤ 1) :
  x + (1 / x ^ 2) ≥ 2   :=  by sorry

Source