lean_workbook_plus_69081
Disproved⚠️ Retired — specification defect
The Lean statement below does not encode the problem shown on this page, so its
Disprovedstatus carries no information about that problem. Do not import this node or use it as a dependency.
Solve the equation:
Why this node was retired
The posted statement is
theorem lean_workbook_plus_69081 : ∀ x : ℝ, x^4 - 3 * x^3 + 3 * x + 1 = 0 ↔ x = -1 ∨ x = 1 ∨ x = (Real.sqrt 2 + 1) ∨ x = (-Real.sqrt 2 + 1) := by sorry
The inserted quartic root list contains nonroots and omits the golden-ratio pair.
The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.
Proposed corrected statement
Prove the roots are (1±√5)/2 and 1±√2, using the factorization (x²−x−1)(x²−2x−1).
Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.
import Mathlib.Analysis.Complex.Basic
theorem lean_workbook_plus_69081 : ∀ x : ℝ, x^4 - 3 * x^3 + 3 * x + 1 = 0 ↔ x = -1 ∨ x = 1 ∨ x = (Real.sqrt 2 + 1) ∨ x = (-Real.sqrt 2 + 1) := by sorry