Find two natural numbers whose sum is 50 and product is 525.

Let the numbers be x and y.

Given,

Sum of numbers is 50.

⇒ x + y = 50

⇒ y = 50 - x     ………(1)

Given,

Product of numbers is 525.

⇒ xy = 525     ………(2)

Substituting value of y from equation (1) in equation(2), we get:

⇒ x(50 - x) = 525

⇒ 50x - x² = 525

⇒ x² - 50x + 525 = 0

⇒ x² - 35x - 15x + 525 = 0

⇒ x(x - 35) - 15(x - 35) = 0

⇒ (x - 15)(x - 35) = 0

⇒ (x - 15) = 0 or (x - 35) = 0     [Using zero-product rule]

⇒ x = 15 or x = 35.

Substituting value of x in equation (1), we get :

Case 1 :

If x = 15, y = 50 − 15 = 35.

Case 2:

If x = 35, y = 50 − 35 = 15.

Hence, the two natural numbers are 15 and 35.