lean_workbook_plus_17283

Proved

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

Let $a,b,c$ be three positive real numbers. Show that $a^2+b^2+c^2\ge bc+ca+ab+3(a-b)(b-c).$ When does the equality occur?

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_17283 (a b c : ℝ) : a^2 + b^2 + c^2 ≥ b * c + c * a + a * b + 3 * (a - b) * (b - c)   :=  by sorry

Source