Question

Find the two consecutive positive odd integers whose product is 483.

Answer 1

Let the two consecutive positive odd integers be x and (x + 2).

According to the given condition,  

x(x + 2) = 483 

⇒ x² + 2x – 483 = 0 

⇒ x² + 23x – 21x – 483 = 0 

⇒ x(x + 23) – 21(x + 23) = 0 

⇒ (x + 23) (x + 21) = 0 

⇒ x + 23 = 0 or x – 21 = 0 

⇒ x = –23 or x = 21 

∴ x = 21   ...(x is a positive odd integer) 

When x = 21, 

x + 2 = 21 + 2

= 23 

Hence, the required integers are 21 and 23.