lean_workbook_plus_11690

Proved

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

By AM-GM, $a^4+b^2\geq 2a^2b$ \na^2+b^4\geq 2ab^2\n $\frac{a}{a^4 +b^2 }+\frac{b}{a^2 +b^4} \le \frac{a}{2a^2b}+\frac{b}{2ab^2}=\frac{1}{ab}. \blacksquare$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_11690  (a b : ℝ)
  (h₀ : 0 < a ∧ 0 < b) :
  a / (a^4 + b^2) + b / (a^2 + b^4) ≤ 1 / (a * b)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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