Two numbers differ by 4 and their product is 96. Find the numbers.

Let the two numbers be x and y.

According to the question,

x – y = 4 …(i)

Also, x×y = 96

…(ii)

On putting the value of in Eq. (i), we get

⇒ 96 – y² = 4y

⇒ y² + 4y – 96 = 0

⇒ y² + 12y – 8y – 96 = 0

⇒ y(y + 12) – 8(y + 12) = 0

⇒ (y – 8)(y + 12) = 0

⇒ y = – 8 and 12

But y = – 8 can’t be the one number as it is given that the numbers are positive.

Hence, the two numbers are 8 and 12.