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Home » Substitute \( a = 0.04 \) into Equation 1: - Dachbleche24

Substitute \( a = 0.04 \) into Equation 1: - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 The sum of the squares of two consecutive positive integers is 365. What is the product of these two integers?

📌 Then, \( n^2 + (n+1)^2 = 365 \).

📌 Expanding, \( n^2 + n^2 + 2n + 1 = 365 \) → \( 2n^2 + 2n + 1 = 365 \).

📌 Subtracting 365: \( 2n^2 + 2n - 364 = 0 \) → divide by 2: \( n^2 + n - 182 = 0 \).

📌 Factoring: \( (n + 14)(n - 13) = 0 \).

📌 Since \( n > 0 \), \( n = 13 \), so the integers are 13 and 14.

📌 Their product is \( 13 \times 14 = 182 \).

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