lean_workbook_plus_62

import Mathlib.Analysis.Complex.Basic

theorem lean_workbook_plus_62 : ∀ a b c : ℝ, 3 * (a ^ 2 * b + b ^ 2 * c + c ^ 2 * a) ≤ (a * b + b * c + c * a) ^ 2 ∧ (a * b + b * c + c * a) ^ 2 ≤ 9   :=  by sorry