if x=3+8^1/2, find x^4+(1/x^4)

x^2 = (3+√8)^2 = 9 + 6√8 + 8 = 17 + 6√8

x^4 = (17+6√8)^2 = 289 + 204√8 + 288 = 577 + 204√8

so x^4 + 1/x^4
= (577 + 204√8) + 1/(577 + 204√8)
= etc (getting messy, work patiently)