a[a^3-(a+1/a-1)]
=（a^4-a^2)+(a-1)
=a^2(a+1)（a-1)+(a-1)
=[a^2(a+1)+1]（a-1)
>0
a[a^3-(a+1/a-1)]>0
a>1>0
所以a^3>(a+1/a-1)