Question

已知m^2-5m-1=0,则2m^2-5m+1/(m^2)=?

Answer 1

m^2-5m-1=0

则m-5-1/m=0

即m-1/m=5

因为（m-1/m）^2=5^2

所以m^2+1/m^2-2=25

即m^2+1/m^2=27

所以2m^2-5m+1/m^2=(m^2-5m-1)+(m^2+1/m^2)+1=0+27+1=28