lean_workbook_plus_18674

Proved

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

Prove or find the counterexample:\n\n $x^6 + y^6 + 4x^3y^3 >= 3y^4x^2 + 3x^4y^2$ \n\n $x, y$ are positive reals.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_18674 (x y : ℝ) (hx : 0 < x) (hy : 0 < y) : x^6 + y^6 + 4 * (x^3 * y^3) ≥ 3 * (y^4 * x^2 + x^4 * y^2)   :=  by sorry

Source