SOLUTION: Find three consecutive even integers such that the sum of the middle two is 1/4 the product of the second and three integers, write an equation and solve.

Question 1133842: Find three consecutive even integers such that the sum of the middle two is 1/4 the product of the second and three integers, write an equation and solve.
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
I assume you mean sum of the first two, not "middle two".
Let x = the middle number
Then the 3 numbers are x-2, x, and x+2
The sum of the first two is x-2 + x = 2x - 2
The product of the last two is x(x+2) = x^2 + 2x
So the equation is:
2x - 2 = (1/4)(x^2 + 2x)
Collect terms and solve:
x^2 - 6x + 8 = 0
This factors as (x-2)(x-4) = 0
Thus x = 2 or x = 4
There are two sequences that meet the conditions:
0, 2, 4 and 2, 4, 6
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