SOLUTION: find three consecutive even integerss such that the square of the largest exceeds the sum of the squares of the other two by 12

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Question 828478: find three consecutive even integerss such that the square of the largest exceeds the sum of the squares of the other two by 12
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
n is an integer, greater than zero.
Three even integers may be 2n, 2n+2, 2n+4.

%282n%2B4%29%5E2=%282n%29%5E2%2B%282n%2B2%29%5E2%2B12
4n%5E2%2B16n%2B16=4n%5E2%2B4n%5E2%2B8n%2B4%2B12
16n%2B16=4n%5E2%2B8n%2B16
16n=4n%5E2%2B8n
4n=n%5E2%2B2n
2n=n%5E2
n%5E2-2n=0
n%28n-2%29=0
The meaningful solution for n is highlight_green%28n=2%29
The three even consecutive integers are 4, 6, and 8.