math question idk how to answer

Question

Determine three consecutive even integers, if the square of the largest integer is 180 less than the sum of the squares of the two smaller integers.

Answer 1

Let's use the variable , x , to represent the smallest of the integers.

The next consecutive even integer would be represented as: (x + 2)

The third consecutive integer would be represented as: (x + 4)

Now based on the info in the problem, we can write and solve the following equation to find the smallest integer first:

Largest integer squared = smallest integer squared + second integer squared minus 180 OR:

(x + 4) ² = x² + (x + 2)² - 180

Now expand the terms and use inverse operations as follows to find the values of x:

x² + 8x + 16 = x² + x² + 4x + 4 - 180

x² + 8x + 16 = 2x² + 4x + 4 - 180

x² + 8x + 16 = 2x² + 4x - 176

x² + 8x + 16 - x² = 2x² + 4x - 176 - x²

8x + 16 = x² + 4x - 176

8x + 16 - 16= x² + 4x - 176 - 16

8x = x² + 4x - 192

8x - 8x = x² + 4x - 192 - 8x

0 = x² - 4x - 192

This factors to (x -16) (x + 12)

x can be 16 or -12

if x is 16, the integers are 16 , 18, and 20

If x is -12, the integers are -12, -10 , -8