The difference of the square of two consecutive even numbers is 84. What is…
2020
The difference of the square of two consecutive even numbers is 84. What is the sum of these two consecutive even numbers?
- A.
34
- B.
38
- C.
36
- D.
42
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Correct answer: D
Let the smaller consecutive even number be x. Then the next consecutive even number is x + 2. According to the question, (x + 2)² - x² = 84. Expanding gives x² + 4x + 4 - x² = 84, so 4x + 4 = 84. Hence 4x = 80 and x = 20. The two numbers are 20 and 22, so their sum is 20 + 22 = 42.