lean_workbook_plus_7029

Proved

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

Prove that $(x^3+y^3)(x+y) \geq (x^2+y^2)^2$ for all positive real numbers $x,y$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_7029 (x y : ℝ) (hx : 0 < x) (hy : 0 < y) : (x ^ 3 + y ^ 3) * (x + y) ≥ (x ^ 2 + y ^ 2) ^ 2   :=  by sorry

Source