Find the two numbers?

Question

Two number's sum is 16. And the sum of their squares is 146. What are the numbers?

Answer 1

The numbers are 5 and 11 and this is a way to solve this:

 

x + y = 16   

 

y = 16 - x   1st equation

 

x² + y² = 146 2nd equation

 

substitute for y (put the first equation in the 2nd equation)

 

x² + (x - 16)² = 146

 

x² + x² - 32x + 256 = 146

 

2x² - 32x + 110 = 0

 

x² - 16x + 55 = 0

 

(x - 5)(x - 11) = 0

 

x = 5 or x = 11

 

they add to 16

 

their squares are 25 and 121 which add to 146

 

Answer 2

Hello Jase

 

x + y = 16

x² + y² = 146

 

from equation 1) y = 16 - x. Substitute in equation 2, you get

 

x² + (16 - x)² = 146

x² + 256 - 32x + x² = 146

2x² - 32x + 256 - 146 = 0

2x² - 32x + 110 = 0

 

Divide by 2

 

x² - 16x + 55 = 0

(x - 5)(x - 11) = 0

 

Therefore, your 2 numbers are 5 and 11. To confirm,

 

5 + 11 = 16

 

5² + 11² = 25 + 121 = 146