x²-3x+1=0
得x=(3±√5)/2
1/x=(3-√5)/2或(3+√5)/2
x+1/x=3
x^4+1 /x^4
=(x²+1/x²)²-2
=[(x+1/x)²-2]²-2
=[3²-2]²-2
=47