Find two consecutive positive integers , Sum of whose square is 365

Let the two consecutive positive integers be \( x \) and \( x + 1 \).

The sum of their squares is given as:
\[
x^2 + (x + 1)^2 = 365
\]

First, expand the equation:
\[
x^2 + (x^2 + 2x + 1) = 365
\]
\[
2x^2 + 2x + 1 = 365
\]

Now, subtract 365 from both sides:
\[
2x^2 + 2x + 1 - 365 = 0
\]
\[
2x^2 + 2x - 364 = 0
\]

Divide the entire equation by 2 to simplify:
\[
x^2 + x - 182 = 0
\]

Now, solve this quadratic equation using the quadratic formula:
\[
x = \frac{-b \

Learn how to find two consecutive positive integers whose sum of squares equals 365 with a detailed step-by-step solution. This problem involves algebraic manipulation and understanding of number theory concepts. Suitable for students in Grades 7-9.

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