lean_workbook_plus_44743

Proved

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

For positives $x$ and $y$ we need to prove that $\frac{1}{x}+\frac{2}{y}\geq\frac{25(x+2y)^2}{(x+2y)^3+48xy^2}$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_44743 (x y : ℝ) (hx : 0 < x) (hy : 0 < y) : (1/x + 2/y) ≥ 25 * (x + 2 * y) ^ 2 / ((x + 2 * y) ^ 3 + 48 * x * y ^ 2)   :=  by sorry

Source

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

View graph