Deriving a quadratic from a reciprocal equation

Proved

WorkbookSource.problem_46907

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

If $x^3=u$ , then $u-\frac{1}{u}=1\implies u^2=u+1$

Source: InternLM Lean-Workbook, record lean_workbook_46907; Apache-2.0. Complete source proposition preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_46907 {u : ℝ} (h₁ : u - 1/u = 1) : u^2 = u + 1  :=  by sorry

Source