Question

The sum of two numbers is 49 and the sum of its squares is 41. What are the numbers?

Answer 1

the no. sum is 42+7=49
41 is not a square of any digit no.

Answer 2

Answer: The numbers are 4 and 5.

Step-by-step explanation:

Since we have given that

The sum of two number is 9

        ∴ x + y = 9    ------- (1)

The sum of its squares is 41

       ∴ x² + y² = 41  --------(2)

solve eq(1) and eq(2) by substitution  

y = 9-x  

Substitute y into equation (2)

$x^2 + (9-x)^2 = 41\\\\x^2+81+x^2-18x=41\\\\2x^2-18x+81-41=0\\\\2x^2-18x+40=0\\\\x^2-9x+20=0\\\\x^2-4x-5x+20=0\\\\x(x-4)-5(x-4)=0\\\\x=4,5$

Hence, the numbers are 4 and 5.