lean_workbook_plus_1434

Proved

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

Let $a,b,c\ge 0$ and $a^3+b^3+c^3=a+b+c$ . Prove that \n

a^2+b^2+c^2\leq 3

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_1434 (a b c : ℝ) (ha : a ≥ 0 ∧ b ≥ 0 ∧ c ≥ 0) (hab : a + b + c = a^3 + b^3 + c^3) : a^2 + b^2 + c^2 ≤ 3   :=  by sorry

Source