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

44, 46

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