SOLUTION: Answers for The Difference Between The Squares Of Two Consecutive Even Number Is 44

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Question 833149: Answers for The Difference Between The Squares Of Two Consecutive Even Number Is 44
Found 2 solutions by josgarithmetic, JulietG:
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
2n and 2n+2 are some even, consecutive numbers.

%28%282n%29%2B%282n%2B2%29%29%28%282n%29-%282n%2B2%29%29=44
%282n%29%5E2-%282n%2B2%29%5E2=44
4n%5E2-%284n%5E2%2B8n%2B4%29=44
4n%5E2-4n%5E2-8n-4=44
-8n-4=44
-8n=48
highlight%28n=-6%29


ANSWER: The numbers would be -12 and -10.
Does this work?
%28-12%2B%28-10%29%29%28-12-%28-10%29%29
%28-12%29%5E2-%28-10%29%5E2
144-100
44, YES.

Answer by JulietG(1812) About Me  (Show Source):
You can put this solution on YOUR website!
a^2 - b^2 = 44
a = B + 2 (because it's even)
Substitute the a value
(b+2)^2 - b^2 = 44
(b+2)(b+2) - b^2 = 44
(b^2 + 2b + 2b + 4) - b^2 ==
add the bs
b^2 + 4b +4 - b^2 = 44
subtract
4b + 4 = 44
Subtract 4 from each side
4b = 40
Divide by 4
b = 10
.
If B is 10, then A is 10+2=12
.
Let's check it
12^2 - 10^2 = 44
(12*12) - (10*10) = 44
144 - 100 does indeed equal 44
Success!