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2 years ago

15

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

egers.

1 answer:

koban [17]2 years ago

3 0

Answer:

4 and 6 or -6 and -4

Step-by-step explanation:

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

<u>We have:</u>

(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

<u>The numbers are:</u>

4 and 6 or - 6 and - 4

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