lean_workbook_plus_74141

Proved

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

For $x < 0$ , prove that $f(x) = x^2 + x + \frac{1}{x} + \frac{1}{x^2} \geq 0$ with equality at $x = -1$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_74141 (x : ℝ) (hx : x < 0) : x^2 + x + 1/x + 1/(x^2) ≥ 0   :=  by sorry

Source