lean_workbook_plus_63494

Proved

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

Let $a$ be a positive real number such that: $a^3= 6(a + 1)$ Prove that this equation $x^2 + ax + a^2 - 6 = 0$ doesn't have real solution.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_63494 (a : ℝ) (ha : a > 0) (hab : a^3 = 6 * (a + 1)) : ¬ ∃ x : ℝ, x^2 + a * x + a^2 - 6 = 0   :=  by sorry

Source