Let `a >2` be a constant. If there are just 18 positive integers satisfying the inequality `(x-a)(x-2a)(x-a^2)<0,` then the value of `a` is ____________

Explanation

As `a gt 2` Hence
`a^2 gt 2a gt a gt 2 `
Hence , the solution set is as follows :
Between (0,a) ther are (a-1) positive interger between `(2a ,a ^2) ` there are `a^2- 2a -1 ` itnergers ,.Therefore
`a^2-2a-1+a-1=18`
or `a^2-a-20=0`
or `(a-5)(a+4)=0`
`rArr a=5`