Question

the sum of 3 consecutive integer is equal their product . find the numbers.

Answer 1

Let the three consecutive integers be x-1, x and x+1.

Therefore,

$x - 1 + x + x + 1 = x(x - 1)(x + 1) \\ 3x = x( {x}^{2} - 1) \\ x( {x}^{2} - 1) - 3x = 0 \\ x( {x }^{2} - 1 - 3) = 0 \\ x( {x}^{2} - 4) = 0 \\ x =0 \\ x = 2 \\ x = - 2$
These are the possible values of x.

Now the consecutive integers are x-1, x and x+1.

Therefore
possible set of integers are:

(-1, 0, 1), (1, 2, 3) or (-3, -2, -1).

Answer 2

the 3 pairs are

1,2,3

-1,-2,-3

-1,0,1