如果m平方-3m+1=0 求m的4次方+m的4次方分之1的值

m平方-3m+1=0 ,m平方+1=3m;
m的4次方+m的4次方分之1
=(m²+1/m²)²-2
=[(m+1/m)²-2]²-2
=[(m²+1)/m)²-2]²-2
=[(3m)/m)²-2]²-2
=[(3)²-2]²-2
=(9-2)²-2
=49-2
=47