The sum of the squares of two natural consecutive odd numbers is 394. The sum of the numbers is ___ - mathselab.com

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

Question

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


A. 40
B. 30
C. 28
D. 24


Answer: C

Solution:

We know that x^2 + (x + 2)^2 = 394

=> x^2 + x^2 + 4x + 4 = 394

=> 2 x^2 +4x – 390 = 0

=> x^2 + 2x – 195 = 0

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

=> x = 13

We know Required sum = 13 +15 =28

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