Question

The difference of two natural numbers is 9 and there product is 112.Find the number .​

Answer 1

Given: The difference of two natural numbers is 9 and their product is 112.

To find: The natural number

Explanation: Let the numbers be x and y, where x is greater than y.

We know that, difference of numbers = 9

x-y = 9 -eq. (i)

And, product of numbers = 112

x * y = 112 -eq. (ii)

Squaring equation (i), we get,

(x-y)^2 = 9^2

x^2 + y^2 - 2 * x * y= 81 - eq. (iii)

Putting eq. (ii) in eq. (iii), we get,

x^2 + y^2 = 81 + 224

x^2 + y^2 = 305

Adding 2xy on both sides, we get,

x^2 + y^2 + 2 * x * y = 305 + 224

(x+y)^2 = 529

x+y = 23 - eq. (iv)

Adding eq. (i) and (iv), we get,

x -y + x +y = 9+ 23

2x = 32

x= 16

And, y= 7.

The numbers are 16 and 7.