A quadratic symmetric value from a difference of cubes

Proved

WorkbookSource.problem_9978

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

lean-workbooksource-checked

Find the value of $a^2+ab+b^2$ given $a^3-b^3=24$ and $a-b=2$

Source: InternLM Lean-Workbook, record lean_workbook_9978 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_9978 (a b : ℝ) (h₁ : a^3 - b^3 = 24) (h₂ : a - b = 2) : a^2 + a * b + b^2 = 12  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_9978; Apache-2.0

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