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Evernote2onenote Tool -

📅 May 7, 2026 👤 scraface

May 07, 2026

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The equation is \( n^2 + (n+1)^2 = 85 \).
This expands to \( n^2 + n^2 + 2n + 1 = 85 \).
Combine like terms: \( 2n^2 + 2n + 1 = 85 \).
Subtract 85: \( 2n^2 + 2n - 84 = 0 \).
Factor: \( (n-6)(n+7) = 0 \).
Solutions are \( n = 6 \) and \( n = -7 \).
The integers are 6 and 7, or -7 and -6.
#### 6, 7 or -7, -6
Here, \( a = 5 \), \( b = 12 \).
So, \( 5^2 + 12^2 = c^2 \).

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