Question

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

Answer 1

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` + `(14 - x)^2` = 148
`x^2` + `x^2` - 28x + 196 = 148
`2x^2` - 28x + 48 = 0
`2x^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