The sum of two numbers is 9 and the sum of their squares are 41. The numbers are:

Correct option is A

Given:

Sum of two numbers: x + y = 9

Sum of their squares: x$$^2$$​ + y$$^2$$​ = 41

Concept Used:

(x + y)$$^2$$​ = x$$^2$$​ + y$$^2$$​ + 2xy

Solution: 

Now, 

2xy = (x + y)$$^2$$​ - (x$$^2$$​ + y$$^2$$​)

2xy = 9$$^2$$​ - 41

2xy = 81 - 41 = 40

xy = 20

So, 

Sum of number = 9 

Product of numbers, xy = 20 

So, 

t$$^2$$​ - 9t + 20 = 0

(t - 5)(t - 4) = 0

The numbers are 5 and 4.