lean_workbook_plus_27006

Proved

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

Let $a,b,c > 0$ such that $a + b + c = 3$ . Prove that \n ${a^2} + {b^2} + {c^2} + a{b^2} + b{c^2} + c{a^2} \ge 6$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_27006 (a b c : ℝ) (ha : a > 0 ∧ b > 0 ∧ c > 0 ∧ a + b + c = 3) : a^2 + b^2 + c^2 + a * b^2 + b * c^2 + c * a^2 ≥ 6   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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