lean_workbook_plus_69800

Proved

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

Let $a,b,c,d$ be nonnegative real numbers such that $a^3+b^3+c^3+d^3+abcd=5.$ Prove that $ab+cd \leq 2.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_69800 (a b c d : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (hd : 0 ≤ d) (habc : a * b * c * d = 1) (h : a^3 + b^3 + c^3 + d^3 + a * b * c * d = 5) : a * b + c * d ≤ 2   :=  by sorry

Source

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

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