SOLUTION: The product of the smallest and largest of three consecutive even integers is three times the middle integer. Find the integers.

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Question 1166829: The product of the smallest and largest of three consecutive even integers is three times the middle integer. Find the integers.
Answer by ikleyn(52804) About Me  (Show Source):
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Let x be the middle of the three consecutive even integers.


Then (x-2) and (x+2) are two other "extreme" integers.


The equation, from the condition, is


    (x-2)*(x+2) = 3x,  or

    x^2 - 4     = 3x

    x^2 - 3x - 4 = 0


Factor left side


    (x-4)*(x+1) = 0.


Of the two roots x= 4 and x= -1, only x= 4 satisfies the condition to be even integer number.


ANSWER.  The numbers are 2, 4 and 6.

Solved.