Question

If x, y, z are non-negative real numbers satisfying `x+y+z=1`, then the minimum value of `((1)/(x)+1)((1)/(y)+1)((1)/(z)+1)`, is
A. 8
B. 16
C. 32
D. 64

Answer 1

Correct Answer - D
From the above example, we have
`(1)/(x)+(1)/(y)+(1)/(z)ge9`
Also, by using `A.M.geG.M.,` we have
`implies" "(x+y+z)/(3)ge(xyz)^(1//3)`
`implies" "(1)/(xyz)ge27" "[becausex+y+z=1]`
Now, `((1)/(x)+1)((1)/(y)+1)((1)/(z)+1)`
`=1+(1)/(x)+(1)/(y)+(1)/(z)+(x+y+z)/(xyz)+(1)/(xyz)ge1+9+27+27=64`