lean_workbook_plus_14061

Proved

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

Let $a,b$ are positive real number such that $a+b=2.$ Prove that

\frac{1}{a^2+3}+\frac{1}{b^2+3}\leq \frac{1}{2}

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_14061 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) (hab : a + b = 2) : 1 / (a^2 + 3) + 1 / (b^2 + 3) ≤ 1 / 2   :=  by sorry

Source