lean_workbook_plus_6548

Proved

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

Let $x,y > 0$ such that $x^5 + y^5 = 2$ . Prove that : $(x^2 + y^6)(x^8 + y^4) + 2\ge x^{10} + y^{10}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_6548 (x y : ℝ) (hx : 0 < x) (hy : 0 < y) (h : x^5 + y^5 = 2) : (x^2 + y^6)*(x^8 + y^4) + 2 ≥ x^10 + y^10   :=  by sorry

Source