Question

How to find the consecutive numbers whose squares differ by 17?

A) Solve a quadratic equation
B) Use the difference of squares formula
C) Apply the Pythagorean theorem
D) Set up and solve a system of linear equations

Answer 1

To find the consecutive numbers whose squares differ by 17, set up and solve a system of linear equations. The consecutive numbers are 8 and 9.

Step-by-step explanation:

To find the consecutive numbers whose squares differ by 17, we can set up and solve a system of linear equations.

1. Let's assume the first number is x.
2. The consecutive number will be x+1.
3. We can set up the equation (x+1)^2 - x^2 = 17.
4. Expanding and simplifying the equation, we get 2x + 1 = 17.
5. Solving for x, we find that x = 8.
6. Therefore, the consecutive numbers are 8 and 9.