Question

The sum of the squares of two consecutive odd positive integers is 394. Find them.

Answer 1

Let’s assume the consecutive odd positive integer to be 2x – 1 and 2x + 1 respectively. [Keeping the common difference as 2]

Now, it’s given that the sum of their squares is 394.

Which means,

(2x – 1)² + (2x + 1)² = 394

4x² +1 – 4x + 4x² +1 + 4x = 394

By cancelling out the equal and opposite terms, we get

8x² + 2 = 394

8x² = 392

x² = 49

x = 7 and – 7

Since we need only consecutive odd positive integers, we only consider x = 7.

Now,

2x – 1 = 14 -1 = 13

2x + 1 = 14 + 1 = 15

Thus, the two consecutive odd positive numbers are 13 and 15 respectively.