lean_workbook_plus_76597

Proved

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

Let $x, y$ be positive real numbers satisfying $x+y=1.$ Prove that $\frac{2}{x+3y}+\frac{1}{2x+y} \geq \frac{8}{5}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_76597 (x y : ℝ) (hx : 0 < x) (hy : 0 < y) (hxy : x + y = 1) : 2 / (x + 3 * y) + 1 / (2 * x + y) ≥ 8 / 5   :=  by sorry

Source