lean_workbook_plus_52840

Proved

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

Prove the inequality $(1)\ \ \frac {a(3a + 1)}{(a + 1)^2}\leq \frac{3}{4}a+\frac{1}{4}$ for positive real numbers $a$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_52840 (a : ℝ) (ha : 0 < a) : (a * (3 * a + 1)) / (a + 1) ^ 2 ≤ (3 / 4 : ℝ) * a + 1 / 4   :=  by sorry

Source