lean_workbook_plus_45452

Proved

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

Let $k_1, k_2, a,b \in R^{ + }$ . Prove that \n $k_1 k_2 a^3 + (k_1^2 + k_2^2 + k_1k_2)(a^2b + ab^2) + k_1 k_2 b^3 \le \frac {(k_1 + k_2)^2 (a + b)^3}{4}$ \n \n What is the generalized form?

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_45452 (k₁ k₂ a b : ℝ) (hk₁ : 0 < k₁) (hk₂ : 0 < k₂) (ha : 0 < a) (hb : 0 < b) : k₁ * k₂ * a ^ 3 + (k₁ ^ 2 + k₂ ^ 2 + k₁ * k₂) * (a ^ 2 * b + a * b ^ 2) + k₁ * k₂ * b ^ 3 ≤ (k₁ + k₂) ^ 2 * (a + b) ^ 3 / 4   :=  by sorry

Source

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

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