Adding two cubic terms

Proved

WorkbookSource.problem_21745

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

lean-workbooksource-checked

Given $\sqrt{x}=a^3-4=4-b^3$ , show that $a^3+b^3-8=0$

Source: InternLM Lean-Workbook, record lean_workbook_21745 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_21745 (x a b : ℝ) (hx : x ≥ 0 ∧ a^3 - 4 = 4 - b^3) : a^3 + b^3 - 8 = 0  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_21745; Apache-2.0

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