Prove2Me

lean_workbook_plus_6070

Proved

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

Use identity: 3(x5+y5+z5)=3(x+y+z)5+5(x2+y2+z2+xy+yz+zx)(x3+y3+z3−(x+y+z)3)3(x^{5}+y^{5}+z^{5})=3(x+y+z)^{5}+5(x^{2}+y^{2}+z^{2}+xy+yz+zx)(x^{3}+y^{3}+z^{3}-(x+y+z)^{3})

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_6070 (x y z : ℝ) : 3 * (x ^ 5 + y ^ 5 + z ^ 5) = 3 * (x + y + z) ^ 5 + 5 * (x ^ 2 + y ^ 2 + z ^ 2 + x * y + y * z + z * x) * (x ^ 3 + y ^ 3 + z ^ 3 - (x + y + z) ^ 3)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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