What are three consecutive numbers that have the same total and product?

I was thinking te equation was :





x + (x+1) + (x+2) = x * x * x * 2 * 1





But if it's not -- then how do u solve the equation?What are three consecutive numbers that have the same total and product?
n +(n+1)(n+2) =n(n+1)(n+2)


3(n+1) = n(n+1)(n+2); simplify ny (n+1) to get


3 = n(n+2)


n^2 +2n -3 = (n -1)(n+3) --%26gt;


n =1 or n =-3





There are 3 sets of numbers





1st set of numbers :


1 ; 2 ; 3





*************


2nd set of numbers :


-3 ; -2 ; -1





***************


3rd set of numbers :


-1 ; 0 ; 1What are three consecutive numbers that have the same total and product?
T = x + x +1 + x + 2 = 3 x + 3 = 3(x + 1)





P = x (x + 1)(x + 2)





P = T so x(x+1)(x+2) = 3(x+1)





x(x+2)-3=0 Factoring (x-1)(x+3) so x=1 or -3





The sequence then is 1, 2, 3 or -3,-2,-1
x + (x+1) + (x+2) = x * (x+1) * (x+2)
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Ma'a Salaamah
(x-1) + (x) + (x+1) = (x-1)(x)(x+1)


3x = x(x^2 - 1)


x^3 - 4x = 0


x(x^2 - 4) = 0


x(x+2)(x-2) = 0


x = 0, x = +-2





set 1, x = 0


(-1, 0, 1)





set 2, x = -2


(-3, -2, -1)





set 3, x = 2


(1, 2, 3)
x + (x + 1) + (x + 2) = x(x + 1)(x + 2)





3x + 3 = x(x^2 + 3x + 2)


3x + 3 = x^3 + 3x^2 + 2x


x^3 + 3x^2 - x - 3 = 0


x^2(x + 3) -1(x + 3) = 0


(x^2 - 1)(x + 3) = 0


(x - 1)(x + 1)(x + 3) = 0


x = 1 or x = -1 or x = -3





integers are: -1, 0, 1


or: 1, 2 ,3


or -3, -2, -1
I don't know what the equation would be but the answer is 1, 2, and 3. Hope I helped!!
x + (x+1) + (x+2) = x(x+1)(x+2)


you were on the right path until you try to represent the product, okay


so


3x + 3 = x(x^2 + 3x + 2)


3x + 3 = x^3 + 3x^2 + 2x


bring left over to the right and reverse it


x^3 +3x^2 -x - 3 = 0


now factor, try (x-1)


(x-1)(x^2 + 4x +3) = 0


now reduce quadratic by factoring


(x-1)(x+1)(x+3) = 0


so x could be -3, -1, or 1


check


(-3) + (-2) + (-1) = (-3)(-2)(-1) both sides equal -6..good


(-1) + (0) + (1) = (-1)(0)(1) both sides equal zero, also good


(1) + (2) + (3) = (1)(2)(3) both sides equal 6


and therer you go .... x = -3, -1 and 1 toanswer the question
x+x+1+x+2 = x*(x+1)(x+ 2)





3x+3 = x3 +3x2+2x


x+3 = x2 (x+3)


x=3 / x+3 = x2


1= x2


x=1
lol..idk but r u on math a or algebra?

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