Question

已知函数f(x)=2+1/a-1/(a²x),设0

Answer 1

f(x)为增函数

f(m)=m

f(n)=n

2+1/a-1/(a^2m)=m

2+1/a-1/ (a^2n)=n

1/(2+1/a-m)=a^2m

2a^2m+am-a^2m^2=1

a^2m^2+2am(a+1/2)-1=0

(am+a+1/2)^2-(a+1/2)^2-1=0

mmin=-(a+1/2)^2-1

[an-(a+1/2)]^2+(a+1/2)^2-1=0

nmax=(a+1/2)^2-1

于是n-m最大=2(a+1/2)^2