Question

The difference between two natural numbers is 16. The product of these natural numbers is 192. Find these numbers.

Answer 1

the two numbers are 24 & 8 .

Explanation:

Here we have , The difference between two natural numbers is 16. The product of these natural numbers is 192.We need to Find these numbers. Let's find out:

Let two numbers be x & y , So The difference between two natural numbers is 16 , i.e.

⇒
`x-y = 16` ...........(1)

The product of these natural numbers is 192 , i.e.

⇒
`xy=192`

We know that ,
`(x+y)^2 = (x-y)^2+4xy` i.e.

⇒
`(x+y)^2 = (16)^2+4(192)`

⇒
`(x+y)^2 = 1024`

⇒
`x+y = \pm 32` { Since sum can't be negative as both numbers are positive }

⇒
`x+y = 32` ........(2)

Adding (1) & (2) :

⇒
`(x-y)+(x+y) = 16+32`

⇒
`2x=48`

⇒
`x=24`

So , y = 32-x = 32-24 = 8

Therefore , the two numbers are 24 & 8 .