The sum of the squares of two consecutive odd numbers is 394. The sum of the numbers is?

The sum of the squares of two consecutive odd numbers is 394. The sum of the numbers is?

Explanation

Let the two consecutive odd numbers be x and x + 2.

Given x² + (x + 2)² = 394:

x² + x² + 4x + 4 = 394

2x² + 4x - 390 = 0

x² + 2x - 195 = 0

(x + 15)(x - 13) = 0

x = -15 or x = 13

For x = 13, the numbers are 13 and 15.

13² + 15² = 169 + 225 = 394

The sum of the numbers is 13 + 15 = 28.