Question

The difference between two natural numbers is 4 and their product is 96 which is the smallest number in this

Answer 1

Answer

12 and 8

Explanation

Let the natural numbers be m and n. (m > n)

Given that their difference is 4

⇒ m - n = 4

⇒ m = 4 + n .............(1)

Also, given that their product = 96

⇒ mn = 96

⇒ (n + 4)n = 96 (from 1)

⇒ n² + 4n = 96

⇒ n² + 4n - 96 = 0

⇒ n² + 12n - 8n - 96 = 0 (splitting the middle term)

⇒ n(n + 12) - 8(n + 12) = 0

⇒ (n - 8)(n + 12) = 0

⇒ n = 8 or n = -12

Since n is a natural number, it can;t be negative, hence n = 8

⇒ m = n + 4 = 8 + 4 = 12

Thus, the two numbers are 12 and 8.

Answer 2

Answer:

Natural no. can't be negative one so

X=12 and Y=8

Smallest no among these is 8.

Refer the attachment for explanation.