# What are two consecutive numbers whose product is 552 ?

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Let us assume that the first number is x.

Then, the other number is x+1 because the numbers are consecutive.

Given that the product of the numbers is 552.

Then we will write:

x * (x+1) = 552

\Let us open the brackets:

==> x^2 + x = 552

==> x^2 + x - 552 = 0

Now we will use the formula to solve for x.

==> x = ( -1 + sqrt(1+4*552) /2 = ( -1 + 47) /2 = 46/2 = 23

==> x1= 23

==> x2=(-1-47)/2 = -48/2 = -24

**Then, the numbers are:**

**23 and 24 **

**OR :**

**-23 and -24**

Let us assume that the 1st number is x,and the 2nd number be y.

then, we have

xy = 552

or x = 552/y.....(1)

Also,the 2 no. are consecutive.

Thus, y = x+1

or x = y-1...(2)

From the 2 eqn.,we have

552/y = y-1.

or 552 =y^2 - y

or y^2 - y - 552 = 0.

or y^2 - 24y + 23y - 552=0

ie y(y-24) + 23(y-24)= 0

ie (y+23)(y-24)=0

therefore, we have y = -23 or y = 24.

Thus,

there can be two possibilities,

when y=-23, x = -24.And when y = 24, x = 23.