Question

Find two consecutive numbers whose squares differ by 17.

Answer 1

-9 and -8

8 and 9

Explanation:

The difference between the squares of two consecutive integers j and j+1 is |2j+1|. There are two pairs where this quantity is 17:

-9 and -8

8 and 9

Answer 2

8 and 9

Explanation:

Hello!

Let the first of the two consecutive numbers be x. The second number would be x + 1.

The equation would be: (x + 1)² - x² = 17, as we subtract the squares to get 17.

Solve for x

• (x + 1)² - x² = 17
• x² + 2x + 1 - x² = 17
• 2x + 1 = 17
• 2x = 16
• x = 8

The first number is 8, so the second number would be 9.

____________________________

We can confirm this by subtracting the square of 8 by the square of 9, and see if it equals 17.

• 9² - 8² = 17
• 81 - 64 = 17
• 17 = 17

Our answer is correct.