lean_workbook_plus_28706

Proved

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

Prove that $x, y, z\in R_{+} \wedge xyz\ge1 \implies \frac{x}{x+y+z}\ge \frac{x^2}{x^5+y^2+z^2}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_28706 (x y z : ℝ) (hx : x > 0 ∧ y > 0 ∧ z > 0 ∧ x*y*z ≥ 1) : x/(x+y+z) ≥ x^2/(x^5+y^2+z^2)   :=  by sorry

Source