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?

1 Answer
Jul 11, 2018

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.