lean_workbook_plus_53058

Proved

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

For 2), if $x + y + z = 0$ , then prove that\n(i) $x^4 + y^4 + z^4 = 2(xy + yz + zx)^2$ \n(ii) $x^5 +y^5 + z^5 = -5xyz(xy + yz + zx)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_53058 (x y z : ℝ) (h : x + y + z = 0) : (x^4 + y^4 + z^4 = 2 * (x * y + y * z + z * x)^2 ∧ x^5 + y^5 + z^5 = -5 * x * y * z * (x * y + y * z + z * x))   :=  by sorry

Source

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

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