lean_workbook_plus_39026

Proved

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

For positive real numbers $a,b$ , prove that $\frac{1}{3a+b}+\frac{1}{a+3b} \leq \frac{1}{4}(\frac{1}{a} + \frac{1}{b}).$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_39026 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) : 1 / (3 * a + b) + 1 / (a + 3 * b) ≤ (1 / 4) * (1 / a + 1 / b)   :=  by sorry

Source