X^3-2X+4
=X（X^2+X-1）-（X^2+X-1）+3
=3
a^4+1/a^4
=a^4+1/a^4+2-2
=(a^2+1/a^2)^2-2
因为a^2-3a+1=0 a不等于0
a^2+1=3a两边同除以a
所以a+1/a=3
所以(a^2+1/a^2)^2-2
=[（a+1/a）^2-2]^2-2
=(3*3-2)^2-2
=47