The sum of two numbers is 16, and the sum of their squares is 146. Find the two numbers.

Question

pls. help if u know

Answer 1

Let's call the numbers x and y.

 

Then, x+y = 16 and x²+y² = 146

 

Since x+y = 16, y = 16-x

 

So, x² + (16-x)² = 146

 

x² + 256 - 32x + x² = 146

 

2x² - 32x + 110 = 0

 

x² - 16x + 55 = 0

 

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

 

x = 11 or x = 5

 

If x = 11, then y = 16-x = 5

 

If x = 5, then y = 16-x = 11

 

The numbers are 5 and 11.