a^2-7a-1=0,a^2=7a+1
a^2+1/a^2
=7a+1+1/(7a+1)
=(49a^2+14a+2)/(7a+1)
=(49a^2+2a^2)/a^2
=51
a^4+1/a^4
=(a^2+1/a^2)^2-2
=51*51-2
=2601-2
=2599