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Home » Solution: Use the Euclidean algorithm: - Rice University

Solution: Use the Euclidean algorithm: - Rice University

📅 May 14, 2026 👤 scraface

May 14, 2026

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\Rightarrow x^2 + rac{1}{x^2} = 7
Next, square this new result to find $ x^4 + rac{1}{x^4} $:
\left( x^2 + rac{1}{x^2}
ight)^2 = 7^2
\Rightarrow x^4 + 2 + rac{1}{x^4} = 49
\Rightarrow x^4 + rac{1}{x^4} = 47
Thus, the value is $ oxed{47} $.
Question: Expand the product $ (2a - 3b)(4a^2 + 6ab + 9b^2) $.
Solution: We recognize that this is a sum of cubes pattern:
Compute each cube:

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