The product of two numbers is 192 and the sum of these two numbers is 28. What is the smaller of these two numbers?

Let the two numbers be x and y .
According to question,
∴ xy = 192...................... (1)
x + y = 28........................(2)
As we know that,
(x - y)² = (x + y)² - 4xy
Put the value of xy and x + y from equation (1) and (2), we will get
(x - y)² = (28)² - 4 x 192
⇒ (x - y)² = 784 - 786
⇒ (x - y)² = 16
⇒ x - y = 4......................(3)
Add the equation (2) and (3), we will get
x + y + x - y = 28 + 4
2x = 32
x = 16
Put the value of x in equation (2), we will get
16 + y = 26
y = 28 - 16
y = 12
So numbers are x = 16 and y = 12.
Smaller number is 12.