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

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(52879) (Show Source): You can put this solution on YOUR website!
.

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.

RELATED QUESTIONS
The sum of a number and three times another number is 18. Their product is a maximum.... (answered by checkley71)

th sum of four consecutive whole numbers is 150. a- let x represent the first number.... (answered by checkley77)

1. The sum of 4 integers is 24 and their product is 945. What are those integers? 2.... (answered by CPhill,greenestamps)

(1) One number is four greater than another number. The sum of the two numbers is 78.... (answered by solver91311)

Three numbers are in arithmetic progression,their sum is15and their product is... (answered by ikleyn)

Three quarter the product of 2 numbers x and y (answered by macston)

The sum of a number and three times another number is 30. Their product is a maximum.... (answered by ikleyn)

The sum of two numbers is 133. Four times the smaller of the two numbers equals three... (answered by dudeantariksh,KaitieB)

The sum of three consecutive natural numbers is 963, find the numbers. (A) First,... (answered by Timnewman)