Find the sum of two consecutive even numbers, the difference of which square is 84?
- 44
- 46
- 42
- None of these
Explanation
We know that the difference of their squares is 84, so we can write the equation:
(x+2)^2 - x^2 = 84
Expanding the equation, we get:
x^2 + 4x + 4 - x^2 = 84
Simplifying the equation, we get:
4x + 4 = 84
Subtracting 4 from both sides, we get:
4x = 80
Dividing both sides by 4, we get:
x = 20
So, the two consecutive even numbers are 20 and 22.
The sum of these numbers is:
20 + 22 = 42
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