Question

Two natural number differ by 3 and their product is 504. Find the numbers. 

Answer 1

Let the required numbers be x and (x + 3)

According to the question: 

x(x + 3) = 504 

⇒ x² + 3x = 504 

⇒ x² + 3x – 504 = 0 

⇒ x² + (24 – 21)x – 504 = 0 

⇒ x² + 24x – 21x – 504 = 0 

⇒ x(x + 24) – 21(x + 24) = 0 

⇒ (x + 24)(x – 21) = 0 

⇒ x + 24 = 0 or x – 21 = 0 

⇒ x = –24 or x = 21 

If x = –24, the numbers are –24 and {(–24 + 3) = –21}.

If x = 21, the numbers are 21 and {(21 + 3) = 24}.  

Hence, the numbers are (–24, –21) and (21, 24).