x=m代入方程
m²-3m+1=0
m²=3m-1
(1)
m³-8m+1
=m×m²-8m+1
=m×(3m-1)-8m+1
=3m²-m-8m+1
=3(3m-1)-9m+1
=9m-3-9m+1
=-2
(2)
m² -3m+1=0
等式两边同除以m
m -3 +1/m=0
m +1/m=3
m²+1/m²=(m+1/m)²-2=3²-2=9-2=7
(3)
m²-3m+1=0
m²-3m=-1
1/m -1/(m-3)
=[(m-3)-m]/[m(m-3)]
=(m-3-m)/(m²-3m)
=(-3)/(-1)
=3
(4)
m²-3m+1=0
m²+1=3m
m²-2m=m-1
m²-2m+ 3/(m²+1)
=m-1 +3/(3m)
=m +1/m -1
=3 -1
=2