Question

Find the two consecutive positive even integers whose product is 288. 

Answer 1

Let the two consecutive positive even integers be x and(x+2)
According to the given condition, 

`x(x+2)=288` 

⇒`x^2+2x-288=0` 

⇒`x^2+18x-16x-288=0` 

⇒`x(x+18)-16(x+18)=0` 

⇒`(x+18)(x-16)=0` 

⇒`x+18=0  or  x-16=0` 

⇒`x=-18  or  x=16` 

`∴x=16   `             (x is a positive even integer) 

When` x=16 `

`x+2=16+2=18` 

Hence, the required integers are 16 and 18.