The vector x and y are the lenght of 3units(they both have a magnitude of 3). If the magnitude of( vectorx + vector y)= root 17, determine the magnitude of (vector x- vector y)

Did you make a diagram?

Draw vectors x and y, with Ø as the angle between them.
so we have a triangle with sides 3,3, and √17 with Ø contained between the two equal sides

17 = 9 + 9 - 2(3)(3)cosØ
cosØ =1/18
Ø = 86.81
now draw -vector y
then |x-y| is opposite the angle 180-86.81
let its magnitude be m
m^2 = 9+9-2(3)(3)cos93.185
= 19
m = √19