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📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 The sum of the squares of three consecutive integers is 365. What is the middle integer?

📌 Let the integers be \( n - 1, n, n + 1 \).

📌 Their squares sum to \( (n - 1)^2 + n^2 + (n + 1)^2 = 365 \).

📌 This expands to \( n^2 - 2n + 1 + n^2 + n^2 + 2n + 1 = 365 \).

📌 Simplifying, \( 3n^2 + 2 = 365 \) leads to \( 3n^2 = 363 \).

📌 Thus, \( n^2 = 121 \), so \( n = 11 \) (since \( n \) is an integer).

📌 A right triangle has legs of lengths 8 and 15. What is the length of the hypotenuse?

📌 Using the Pythagorean theorem, \( a^2 + b^2 = c^2 \), where \( a = 8 \) and \( b = 15 \).

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