The sum of two numbers is 22 and the sum of their squares is 404, then the product of those numbers is:

Correct option is D

Given:
x + y = 22
x² + y² = 404
Rearranging the first equation:
y = 22 - x
Substituting the value of 'y' in the second equation:
x² + (22 - x)² = 404
x² + 484 - 44x + x² = 404
2x² - 44x + 80 = 0
Simplifying the quadratic equation:
x² - 22x + 40 = 0
Factoring the equation:
(x - 20)(x - 2) = 0
Therefore, the possible values of 'x' are 20 and 2.
If x = 20, then y = 22 - 20 = 2
If x = 2, then y = 22 - 2 = 20
In either case, the product of the numbers (x x y) = 20 x 2 = 40.