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.

44, 46

Step-by-step explanation:

The integers are both even, so if the smaller one is x, then the larger one is x+2.

Therefore:

((x) + (x+2))² = 4048 + (x)² + (x+2)²

(2x + 2)² = 4048 + x² + x² + 4x + 4

4x² + 8x + 4 = 2x² + 4x + 4052

2x² + 4x - 4048 = 0

x² + 2x - 2024 = 0

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

x = -4+, 44

Since x must be positive, x = 44.  And x+2 = 46.  So the numbers are 44 and 46.

Let's check:

(44 + 46)² = 8100

4048 + 44² + 46² = 8100

24

step-by-step explanation:

answer: 4 (:

step-by-step explanation: