SOLUTION: (X-2),x and (x+2) are three natural numbers.if the product of th three numbers is four times their sum,determine the number

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Question 1091071: (X-2),x and (x+2) are three natural numbers.if the product of th three numbers is four times their sum,determine the number
Answer by ikleyn(52873) About Me  (Show Source):
You can put this solution on YOUR website!
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The product is x*(x-2)*(x+2) = x*(x^2-4).


The sum is (x-2) + x + (x+2) = 3x.


The equation is 

x*(x^2-4) = 3x,

x*(x^2-4) - 3x = 0,

x*(x^2-7) = 0.


It deploys in two independent equations


a) x = 0  with the solution x= 0,   and


b) x^2 - 7 = 0  ====>  x^2 = 7,   which has not integer solutions.


Answer.  The only integer solution is x = 0,  and the integers are -2, 0, and 2.

Solved.