What is the sum of two consecutive even numbers, the difference of whose squares is 84?Choices:- 34 38 42 46
Question
What is the sum of two consecutive even numbers, the difference of whose squares is 84?
Choices:
- 34
- 38
- 42
- 46
Solution
Let's denote the two consecutive even numbers as x and x+2.
The difference of their squares is given by:
(x+2)^2 - x^2 = 84
Expanding and simplifying this equation gives:
4x + 4 = 84
Subtracting 4 from both sides gives:
4x = 80
Dividing both sides by 4 gives:
x = 20
So, the two consecutive even numbers are 20 and 22.
The sum of these two numbers is 20 + 22 = 42.
So, the answer is 42.
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