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

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

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`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

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`

4 views Answered 2023-02-05 15:29