Question

The sum of the squares of two positive numbers is 80 and the difference of the squares of the numbers is 48. How do you find the numbers?

Answer 1

I got `8 and 4`

Explanation:

Let us call the numbers `x` and `y` we get:

`x^2+y^2=80`

`x^2-y^2=48`

let us add the two together:

`(x^2+x^2)+(y^2-y^2)=80+48`

`2x^2=128`

`x^2=128/2=64`

`x=+-sqrt(64)=+-8` Let us choose the positive one and substitute into the first equation for `x`:

`8^2+y^2=80`

`y^2=80-64=16`

`y=+-sqrt(16)=+-4` let us choose again the positive one.