Question

1.已知m^2-5m-1=0,则2m^2-5m+m^-2=?2.已知非负数a.b.c满足条件a+b=7,c-a=5,设S=a+b+c的最大值为m,最小...

1.已知m^2-5m-1=0,则2m^2-5m+m^-2=?2.已知非负数a.b.c满足条件a+b=7,c-a=5,设S=a+b+c的最大值为m,最小值为n,则m-n的值为？

Answer 1

2、由a+b=7,c-a=5可得b+c=12
又因为a.b.c为非负数，所以0<=a<=7
S的最大值m=19，最小值n=12
m-n=7

Answer 2

m²-5m-1=0 =>m-1/m=5
两边平方m²-2+1/m²=25
∴m²+1/m²=27
∴2m²-5m+m^-2=m²-5m+m²+1/m²=1+27=28

c=a+5≥5
S=a+b+c=7+c
c=5时,n=12
a+b=7,a≤7
S=a+b+c=7+c=7+a+5=12+a
a=7时,m=19
∴m-n=7

Answer 3

1.2m^2-5m+m^-2=m^2+(m^2-5m-1)+1+m^-2=m^2+1+m^-2
m^2-5m-1=0,同除以m,得m-1/m=5,平方得m^2-2+m^-2=25,
2m^2-5m+m^2=m^2+1+m^2+1+m^-2=25+3=28