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)`, isA. 8B. 16C. 32D. 64

If x, y, z are non-negative real numbers satisfying `x+y+z=1`, then th

1.	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)`, isA. 8B. 16C. 32D. 64
Answer» 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`

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