The difference of two positive numbers is 6 and the sum of their squares is 90. Find the numbers.
I know the numbers are 3 and 9, but I just don't know how to go about showing the work.
Thanks!
You just need to translate this into a system of equations.
$\displaystyle x-y=6$
$\displaystyle x^2+y^2=90$
So you can start off:
$\displaystyle x=y+6$
$\displaystyle (y+6)^2+y^2=90$
$\displaystyle (y^2+12y+36) +y^2=90$
$\displaystyle 2y^2+12y-54=0$
Do you see how to take it from here?