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Given that x,y,z are positive real numbe...

Given that `x,y,z` are positive real numbers such that `xyz=32`, the minimum value of `sqrt((x+2y)^(2)+2z^(2)-15)` is equal to

A

`6`

B

`8`

C

`9`

D

`12`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `(x^(2)+2xy+2xy+4y^(2)+z^(2)+z^(2))/(6) ge (16x^(4)y^(4)z^(4))^(1//6)`
`(x+2y)^(2)+2z^(2) ge 96`
`(x+2y)^(2)+2z^(2)-15 ge 81`
`:.` Least value of `sqrt((x+2y)^(2)+2z^(2)-15)` is `9`
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