The square of the sum of two given natural numbers is 784 , while the product of the two given numbers is 192. Find the positive difference between the squares of these two given numbers.

Correct option is C

Given:

The square of the sum of two natural numbers is 784:

(x + y)² = 784

The product of the two numbers is 192:

xy = 192

Formula Used:

​$$x^2 - y^2 = (x + y)(x - y)$$​​

Solution: 

Let the two numbers be a and b.

ATQ

(a + b)² = 784

=> a + b = 28

and a × b = 192

Now

(a – b)² = (a + b)² – 4ab

= 784 – 768

= 16

=> a – b = 4

Therefore;

a² – b² = (a + b)(a – b)

= 28 × 4

= 112