lean_workbook_plus_20208

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 $\frac{1}{11+a^{2}}+\frac{1}{11+b^{2}}\leqslant \frac{1}{6}.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_20208 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) (hab : a + b = 2) : 1 / (11 + a^2) + 1 / (11 + b^2) ≤ 1 / 6   :=  by sorry

Source