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 

⇒ x² + 2x – 288 = 0 

⇒ x² + 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.