lean_workbook_plus_58978

Proved

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

Let $x,y>0$ and $xy(x+8y)=20.$ Prove that

x+3y\geq 5

Equality holds when $x=2,y=1.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_58978 (x y : ℝ) (hx : 0 < x) (hy : 0 < y) (h : x * y * (x + 8 * y) = 20) : x + 3 * y ≥ 5 ∧ (x = 2 ∧ y = 1 → x + 3 * y = 5)   :=  by sorry

Source

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

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