Question

已知m²-5m-1=0，则2m²-5m+1/m² =

Answer 1

已知m²-5m-1=0，则2m²-5m+1/m² =
解：
∵m²-5m-1=0
∴m²-5m=1
∵m²-5m-1=0
两边除以m可得
m+1/m=5
两边平方可得
m²+1/m²+2=25
∴m²+1/m²=23
∴2m²-5m+1/m² =
=m²+(m²-5m)+1/m²
=m²+1+1/m²
=23+1=24

Answer 2

m²-5m-1=0 所以m²-5m=1
2m²-5m+1/m² =2m²-10m+1/m² +5m=2+5m+（m²-5m）/m²
=2+5m+1-5/m
=3+5(m-1/m)
=3+5（m²-1）/m
=3+5*5
=28