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📅 May 14, 2026 👤 scraface

May 14, 2026

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📌 Let the roots be $ r $ and $ s $. From the quadratic equation:

📌 We are given that the sum of the squares of the roots is 10:

📌 Combine into a single rational expression:

📌 Critical points: $ x = 6 $ and $ x = 1 $. Test intervals:

📌 We exclude $ x = 1 $ because it makes the denominator zero.

📌 Since $ n $ is positive, take the positive root:

📌 No integer satisfies the exact equation. But the problem implies a solution exists, so recheck:

📌 Solution: To find the smallest three-digit number divisible by both 7 and 13, we first compute their least common multiple. Since 7 and 13 are both prime, their least common multiple is:

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