SOLUTION: Find tree consecutive even integers such that the square of the sum of the smaller two numbers is equal to twice the largest.

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Question 887938: Find tree consecutive even integers such that the square of the sum of the smaller two numbers is equal to twice the largest.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Numbers are 2n, 2n+2, 2n+4.

%282n%2B2n%2B2%29%5E2=2%282n%2B4%29; solve for n and compute the three numbers.
%284n%2B2%29%5E2=4n%2B8
16n%5E2%2B16n%2B4=4n%2B8
4n%5E2%2B4n%2B1=n%2B2
4n%5E2%2B3n-1=0
%284n-1%29%28n%2B1%29=0

For even integers, n can be here -1 or ....?
cross%284n-1=0%29
cross%284n=1%29
cross%28n=1%2F4%29, will not work, because you will not get integers for your numbers.

The numbers are -2, 0, 2.
Only highlight%28n=-1%29 is solution.