lean_workbook_plus_66945

Proved

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

Let $a,b$ are positive real numbers such that $a^5+b^3\leq a^2+b^2.$ Prove that $a(a+b) \leq 2$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_66945 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) (hab : a^5 + b^3 ≤ a^2 + b^2) : a * (a + b) ≤ 2   :=  by sorry

Source