Question

the sum of three consecutive integers is same as their products .find the number

Answer 1

Answer:

SO, LET THE NUMBERS ARE X , X+1 , X+2

SUM OF NUMBERS = PRODUCT OF NUMBERS

==> X+X+1+X+2 = (X)(X+1)(X+2)

==> 3X+3 = X²+X (X+2)

==> 3X+3 = X³+2X²+X²+2X

==> 0 = X³+3X²+2X-3X-3

==> 0 =  X³+3X²-X-3

LET X = 1

SO, (1)³+3(1)²-(1)-3

==>  1+3-3-1

==> SO, 1 IS FACTOR OF X³+3X²-X-3

X = 1 ,

X+1 = 2

X+2 = 3

SO, THREE NUMBERS ARE = 1,2,3

SO, VERIFY=>

X+X+1+X+2 = (X)(X+1)(X+2)

===> 1+2+3 = 1×2×3

==> 6 = 6