Question

The square of the sum of two consecutive positive even integers is greater than the sum of their squares by 48. Find the two integers.​

Answer 1

• 4 and 6 or -6 and -4

Explanation:

Let the numbers are 2x and 2x + 2.

We have:

• (2x + 2x + 2)² = (2x)² + (2x + 2)² + 48
• 4(2x + 1)² = 4x² + 4(x + 1)² + 48
• (2x + 1)² = x² + (x + 1)² + 12
• 4x² + 4x + 1 = x² + x² + 2x + 1 + 12
• 2x² + 2x - 12 = 0
• x² + x - 6 = 0
• (x - 2)(x + 3) = 0
• x = 2, x = -3

The numbers are:

• 4 and 6 or - 6 and - 4