lean_workbook_plus_45833

Proved

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

Let a,b,c be positive real numbers such that $ab+bc+ca=3$ Prove that $a^2+b^2+c^2+3 \ge 2(a+b+c)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_45833 (a b c : ℝ) (h : a * b + b * c + c * a = 3) : a ^ 2 + b ^ 2 + c ^ 2 + 3 ≥ 2 * (a + b + c)   :=  by sorry

Source