x²-4x+1=0,则x≠0
所以方程两边可以同时除以x,得x-4+1/x=0
则x+1/x=4
x&sup4+1/x&sup4
=(x²+1/x²)²-2
=[(x+1/x)²-2]²-2
=(4²-2)²-2
=14²-2
=194