The product of real roots of the equation `|x|^(6/5)-26|x|^(3/5)-27=0` is

Options

A. `-3^(10)`
B. `-3^(12)`
C. `-3^(12//5)`
D. `-3^(21//5)`

Answer

A

Explanation

We have,
`|x|^(6//5)-26|x|^(3//5)-27=0`
`rArr y^(2)-26y-27=0`,where `y=|x|^(3//5)`
`rArr (y-27)(y+1)=0`
`y=27 " "[:' y=|x|^(3//5) lt 0]`
`rArr |x|^(3//5)=3^(3)`
`rArr |x|^(3)=3^(15)rArr|x|=3^(5)`
Thus, real roots of the given equation are given by `|x|=3^(5)`. So, real roots are `3^(5)` and `-3^(5)`. Hence, their product is `-3^(10)`.