The sum of the squares of two consecutive odd numbers is 394. The sum of the numbers is?
- 28
- 40
- 32
- None of these
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.
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