lean_workbook_plus_4739

Proved

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

Let $a$ and $b$ are positive numbers.

\frac{a}{a^4 +b^2 }+\frac{b}{a^2 +b^4} \le \frac{1}{ab}.

Switzerland - Swiss 1998

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_4739 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) : (a / (a ^ 4 + b ^ 2) + b / (a ^ 2 + b ^ 4)) ≤ 1 / (a * b)   :=  by sorry

Source