# The sum of 2 numbers is 14 and the sum of their squares is 148, how do you find the numbers?

Jan 20, 2016

2 and 12

#### Explanation:

Use a systems of equations to solve easily:

Assuming x represents the first number and y the second...

x + y = 14
${x}^{2}$ + ${y}^{2}$ = 148
y = 14 - x
${x}^{2}$ + ${\left(14 - x\right)}^{2}$ = 148
${x}^{2}$ + ${x}^{2}$ - 28x + 196 = 148
$2 {x}^{2}$ - 28x + 48 = 0
$2 {x}^{2}$ - 4x - 24x + 48 = 0
2x(x - 2) - 24(x - 2) = 0
(2x - 24)(x - 2) = 0
x = 12 and 2

So, the two numbers are 12 and 2. If you check them back in the equation for x and y you'll see that they work.

Here is a practice problem:

The sum of two numbers is 19 and the sum of their squares is 205. Find the numbers by writing and solving a system of equations.

Hopefully you understand now