显然a≠0,由a^2-5a+1=0,等式同除以a,得a+1/a=5.(a+1/a)^2=a^2+1/a^2+2=25,所以a^2+1/a^2=23.(a^2+1/a^2)^2=a^4+1/a^4+2=529,所以a^4+1/a^4=527.