数学题：如果x²-3X+1=0,求x^4+1/x^4的值

等式两边同除以x
x-3+1/x=0
x+1/x=3
x^4+1/x^4
=(x²+1/x²)²-2
=[(x+1/x)²-2]²-2
=(9-2)²-2
=49-2
=47