lean_workbook_plus_40486

Proved

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

Let $a,b,c$ be real numbers that $ab+bc+ca=3$ . Prove that: $\frac{1}{a^2+2}+\frac{1}{b^2+2}+\frac{1}{c^2+2}\leq1$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_40486 (a b c : ℝ) (h : a * b + b * c + c * a = 3) : 1 / (a ^ 2 + 2) + 1 / (b ^ 2 + 2) + 1 / (c ^ 2 + 2) ≤ 1   :=  by sorry

Source