Question

The sum of two numbers is 3 and the sum of their squares is 29. what are the numbers?

Answer 1

Step-by-step explanation:

`x + y = 3`

`{x}^(2) + {y}^(2) = 29`

`x = 3 - y`

`(3 - y) {}^(2) + {y}^(2) = 29`

`{y}^(2) - 6y + 9 + {y}^(2) = 29`

`2 {y}^(2) - 6y + 9 = 29`

`2 {y}^(2) - 6y = 20`

`{y}^(2) - 3y = 10`

`{y}^(2) - 3y - 10 = 0`

`(y - 5)(y + 2) = 0`

`y = 5`

or

`y = - 2`

Plug this back in we get either that

`5 + x = 3`

`x = - 2`

or

`x = 5`

So the numbers are

-2 and 5.