SOLUTION: Three consecutive even integers, the square of the first integer is four more than sixteen times the second integer. what are the three integers?

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Question 915375: Three consecutive even integers, the square of the first integer is four more than sixteen times the second integer. what are the three integers?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
n= the first of the 3 consecutive even integers.
So,
n%2B2= the second of the 3 consecutive even integers;
n%5E2= the square of the first integer, and
4%2B16%2A%28n%2B2%29= four more than sixteen times the second integer.
The problem says that
n%5E2=4%2B16%2A%28n%2B2%29
so we work from that equation.
n%5E2=4%2B16%2A%28n%2B2%29
n%5E2=4%2B16%2An%2B16%2A2
n%5E2=4%2B16n%2B32
n%5E2=16n%2B36
n%5E2-16n=36
At this point, we can solve the quadratic equation by "completing the square":
n%5E2-16n=36%29
n%5E2-16n%2B64=36%2B64
n%5E2-16n%2B64=100
%28n-8%29%5E2=100
%28n-8%29%5E2=10%5E2 ---> system%28n-8=10%2C%22or%22%2Cn-8=-10%29 ---> system%28n=10%2B8=18%2C%22or%22%2Cn=-10%2B8=-2%29
Since by "even integers" we usually understand, just positive integers divisible by 2, the only acceptable answer is
highlight%28n=18%29 .
So the three consecutive even integers are highlight%2818%29 , highlight%2820%29 , and highlight%2822%29 .