lean_workbook_plus_7050

Proved

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

If a+b+c>=3, show that: $a^2+b^2+c^2+ab+ac+bc\ge6.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_7050 (a b c : ℝ) (hab : a + b + c ≥ 3) : a ^ 2 + b ^ 2 + c ^ 2 + a * b + a * c + b * c ≥ 6   :=  by sorry

Source