Question

The sum of two natural number is 28 and their product is 192. Find the numbers. 

Answer 1

Let the required number be x and (28 – x).

According to the given condition, 

x(28 – x) = 192 

⇒ 28x – x² = 192 

⇒ x² – 28x + 192 = 0 

⇒ x² – 16x – 12x + 192 = 0 

⇒ x(x – 16) – 12(x – 16) = 0 

⇒ (x – 12)(x – 16) = 0 

⇒ x – 12 = 0 or x – 16 = 0 

⇒ x = 12 or x = 16 

When x = 12,

28 – x = 28 – 12

= 16 

When x = 16,  

28 – x = 28 – 16

= 12 

Hence, the required numbers are 12 and 16.