Question

The sum of two numbers is 18 and the sum of their squares is 170. How do you find the numbers?

Answer 1

7 and 11

Explanation:

`a) x+y=18`

`b) x^2+y^2=170`

`a) y=18-x`

replace y in b)

`b) x^2+(18-x)^2=170`

`x^2+324-36x+x^2=170`

`2x^2-36x+324-170=0`

`2x^2-36x+154=0`

Now you only need to use the quadratic form:

`x=(36+-sqrt(36^2-4*2*154))/(2*2)`

`x=(36+-sqrt(1296-1232))/(4)`

`x=(36+-sqrt(64))/(4)=(36+-8)/(4)`

`x=(36+8)/4 or x=(36-8)/4`

`x=11 or x=7` and `y=18-11=7 or y=18-7=11`

So, the numbers are 7 and 11