If x, y , z are three distinct positive real numbers such that x+ y+ z= 1 then the values of (1/x - 1)(1/y -1 ) (1/z - 1) is? (Answer is 8)

Prameela and vikas answered very well. Yes answer can be solved easily by using Arithmetic and Geometric mean. Download and Learn formulas of Progressions and series. It will help you to solve this question easily. 

Minimum value of (1/x-1)(1/y-1)(1/z-1) will be 8 (I think question should be modified here)
Solution:
As we know, for positive real numbers A.M. >= G.M.
Hence x+y+z >= (xyz)^(1/3) or xyz <= 1/27
Now equality will hold true only when x=y=z=1/3 (As expression will get reduced to (1-x)(1-y)(1-z)/xyz and expression to be minimum xyz should be maximum)
After putting values, we will value of expression as 8.
Hope it will help. :)

Edit: (x+y+z)/3 >= (xyz)^(1/3) (For A.M. >= G.M.)

thank you

x y z are distinct positive number