SOLUTION: The product of two consecutive even integers is equal to 6 times the first. Find the numbers.

Question 947750: The product of two consecutive even integers is equal to 6 times the first. Find the numbers.
Found 2 solutions by Alan3354, DrBeeee:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The product of two consecutive even integers is equal to 6 times the first. Find the numbers.
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n*(n+2) = n*6
n+2 = 6
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
let n = the first even integer.
Then the next even integer is n+2.
We are given that
(1) n*(n+2) = 6n or
(2) n*n + 2n = 6n or
(3) n^2 - 4n = 0 or
(4) n*(n - 4) = 0 which has two roots
(5) n = (0,4)
The first root n = 0 is called the trivial solution because (1) gives us 0 = 0. The solution is
(6) n = 4
Check this using (1).
Is (4*(4+2)=6*4)?
Is (4*6 = 24)?Is (24=24)? Yes
Answer: The two consecutive even integers are 4 and 6.

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