lean_workbook_plus_30162

Proved

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

Let $a,b$ be positive real numbers. Prove that $\frac{a^4+b^4}{a^3+b^3}\geq\frac{a^2+b^2}{a+b}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_30162 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) : (a^4 + b^4) / (a^3 + b^3) ≥ (a^2 + b^2) / (a + b)   :=  by sorry

Source