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Home » Step 3: Combine using Chinese Remainder Theorem - Richter Guitar

Step 3: Combine using Chinese Remainder Theorem - Richter Guitar

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 x^3 + rac{1}{x^3} = \left( x + rac{1}{x}

📌 ight)^3 - 3\left( x + rac{1}{x}

📌 x^3 + rac{1}{x^3} = 5^3 - 3 \cdot 5 = 125 - 15 = 110

📌 Thus, the value is \(oxed{110}\).

📌 An archaeologist deciphers a geometric pattern on a Sumerian artifact where the sum of two dimensions is 10, and the sum of their cubes is 880. Find the product of the dimensions.

📌 Let the dimensions be \( a \) and \( b \). We are given:

📌 \( a + b = 10 \)

📌 \( a^3 + b^3 = 880 \)

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