Evaluating a cubic subject to a quadratic relation

Proved

WorkbookSource.problem_2545

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

lean-workbooksource-checked

Find the value of $2x^{3}-3x^{2}-11x+8$ if when $x^{2}-3x-1=0$ .

Source: InternLM Lean-Workbook, record lean_workbook_2545 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_2545 (x : ℝ) (hx : x^2 - 3*x - 1 = 0) : 2*x^3 - 3*x^2 - 11*x + 8 = 11  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_2545; Apache-2.0

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