Question

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`

Answer 1

Correct Answer - 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`