Question

The sum of Two numbers is 9. The sum of the squares of the numbers is 41. Find the numbers.

Answer 1

Answer:

4 and 5

Step-by-step explanation:

Assuming your 2nd sentence should be: "The sum of the squares of the two numbers is 41"

X + Y = 9   {equation 1}

X² + Y² = 41  {equation 2}

from equation 1:  y = 9-x

Substitute that into equation 2

x² + (9-x)² = 41

x² + 81 - 18x + x²= 41

2x² - 18x + 40 = 0

We can factor out a 2

x² - 9x + 20 = 0

(x-5)(x-4) = 0

x = 5 or 4

checking

Your two numbers are 4 and 5

4² + 5² 

= 16 + 25

= 41