lean_workbook_plus_52745

Proved

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

Factor. \n\n

x^8 - x^7 + x^2 - x + 15 = 0

\n\n

x^6 ( x^2 - x) + 1 (x^2 -x) = -15

\n\n

(x^6 + 1)(x^2 - x) = -15

\n\nSince we have the $x^6$ and $x^2$ we have both factors as $\geq 0$ if we have real numbers. Thus, we can't have negative numbers on the RHS which means that we don't have any real roots. \n\n(Does this work?) \n\nEDIT: For the last part please look at djmathman's proof below.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_52745 : ¬ ∃ x : ℝ, x^8 - x^7 + x^2 - x + 15 = 0   :=  by sorry

Source

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

View graph