Vectors Question from Cambridge ME1. Not sure if worked solution is incorrect when finding the x-value? (1 Viewer)

[hmim]

second image is worked solution. I believe the calculation of x value is incorrect, shouldn't it be the root of that?

 

[Jos:)]

Hey, nah that looks right. If you expand the ((2+/3)x)^2 you will get x^2+4x^2+4x^2/3+3x^2=8 take the x^2 out and then divide the RHS by the bracket (should be 8+4/3) and then root it to get /3-1 (which is the answer in soln u provided)

if u also verify the magnitude by using the mag of vector formula with the final soln u will get 2/2