If x-3/x=sqrt(3) then 9/(x^4)+(x^4)/9 = ?

I got the answer as 7 with both a calculator and in exact closed form using quadratic formula but my son's teacher says there is a way to rearrange the equations to get the answer w/o actually solving for x. I have my doubts. Can anyone see how to do it w/o solving for x first?