The sum of two numbers is 9. The squares of the two numbers is 41. Find the values of the two numbers.

Question

I need help with the question.

Answer 1

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

 

Your two numbers are 4 and 5

 

4² + 5² = 16 + 25 = 41

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