91Ó°ÊÓ

Two consecutive even numbers whose product is $360$.

Let x be the first even number.

As a result, the next even number is $x+2$.

360 is the product of two consecutive even numbers. Set up the equation as follows:

localid="1653834652878" $$\begin{gathered} x\left(x+2\right)=360 \\ {x}^2+2x=360 \\ {x}^2+2x-360=0 \end{gathered}$$

Therefore equation is $x^2+2x-360=0$

Now solve the equation for x by multiplying the left side of the equation by

(x+20)(x-18)=0

Using the "Zero Product Property," set each factor to zero and solve for x.

$$\begin{gathered} x+20=0 \\ x=-20 \end{gathered}$$

or

$$\begin{gathered} x-18=0 \\ x=18 \end{gathered}$$

So, the first pair of consecutive numbers are -20 and -20 + 2 = -18: The second pair of consecutive numbers are 18 and 18 + 2=20

To test the solution, find the product of two consecutive numbers.

(-18) (-20)=360 And (18)(20)=360

Because the product is 360, the solution makes sense.

As a result, the consecutive number pairs are -18, -20 and 18,20.