Question

The square of the sum of two consecutive positive even integers is 4048 more than the sum of the squares of these two numbers. Find the two numbers.

Answer 1

Answer:

44 and 46.

Step-by-step explanation:

Let the 2  numbers be x and x + 2  ( because they are consecutive even numbers). So:

(x + (x + 2))^2 = 4048 + x^2 + (x + 2)^2

(2x + 2)^2  - x^2 - (x + 2)^2 = 4048

4x^2 + 8x + 4  - x^2 - (x^2 + 4x + 4)  = 4048

4x^2 - x^2 - x^2 + 8x - 4x + 4 - 4 = 4048

2x^2 + 4x - 4048 = 0

x^2 + 2x - 2024 = 0

(x - 44)(x + 46) = 0

x = 44 because we are given that it is positive.

Therefore the other number is x + 2 = 46.