Question

The product of two consecutive positive even numbers is 360. Find the numbers.

Answer 1

areLet, x and (x+2) is the two consecutive even numbers.

So, the product of the two positive numbers is 360.

Then according to the problem.

`\begin{gathered} x(x+2)=360 \\ x^2+2x-360=0 \\ x^2+20x-18x-360=0 \\ x(x+20)-18(x+20)=0 \\ (x+20)(x-18)=0 \\ \text{Either,} \\ x+20=0 \\ x=-20 \\ or\text{ } \\ x-18=0 \\ x=18 \end{gathered}`

Since the number is positive then we will take the positive number.

Hence, the numbers arem

`\begin{gathered} x=18 \\ x+2=18+2 \\ =20 \end{gathered}`

So,the two consecutive numbers are, 18 and 20.