lean_workbook_plus_66878

Proved

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

Prove that $x^2 + \dfrac 1{4x} \ge \dfrac{3}{4}$ for $x > 0$ using the Arithmetic Mean-Geometric Mean (AM-GM) inequality.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_66878 (x : ℝ) (hx : x > 0) : x^2 + 1 / (4 * x) ≥ 3 / 4   :=  by sorry

Source