SOLUTION: the product of two consecutive even numbers is 36 times more than the square of the smaller number.find the consecutive numbers.

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Question 637638: the product of two consecutive even numbers is 36 times more than the square of the smaller number.find the consecutive numbers.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Strange wording. There may be a typo. I have two interpretations.

If the problem really meant to say that the product is "36 times the square of the smaller number", which is 36 multiplied times the smaller number, then the smaller number is zero.
With the two consecutive even (integer) numbers represented as n and n+2, the math would be:
n%28n%2B2%29=36n%5E2 --> n%5E2%2B2n=36n%5E2 --> n%5E2%2B2n-n%5E2-2n=36n%5E2-n%5E2-2n --> 0=36n%5E2-n%5E2-2n --> 0=35n%5E2-2n --> 0=%2835n-2%29n
The solutions to that equation are
n=2%2F35 , from 35n-2=0 ---> 35n=2 ---> n=2%2F35
and n=0 .
Since 2%2F35 is not an even integer, the only solution is n=0, if we consider zero to be even. (I do, but it could be controversial).

If the problem really meant to say that the product is "36 more than the square of the smaller number", there should be no "times" in the wording.
In that case, it means that it is 36 added to the square of the smaller number.
Then, calling the smaller number n (we'll make sure it's even at the end),
the next even number would be n%2B2 ,
and the wording translates into the equation
n%28n%2B2%29=n%5E2%2B36
Solving:
n%28n%2B2%29=n%5E2%2B36 --> n%5E2%2B2n=n%5E2%2B36 --> n%5E2%2B2n-n%5E2=n%5E2%2B36-n%5E2 --> 2n=36 --> 2n%2F2=36%2F2 --> highlight%28n=18%29 , which is even.
So the numbers are highlight%2818%29 and highlight%2820%29