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The minimum value of (x^4+y^4+z^2)/(x y ...

The minimum value of `(x^4+y^4+z^2)/(x y z)` for positive real numbers `x ,y ,z` is `sqrt(2)` `2sqrt(2)` `4sqrt(2)` `8sqrt(2)`

A

`sqrt(2)`

B

`2sqrt(2)`

C

`4sqrt(2)`

D

`8sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Using A.M. `ge`. G.M we have
`x^(4) + y^(4) ge 2 x^(2) y^(2)` and `2 x^(2) y^(2) + z^(2) ge sqrt(8)xyz`
`implies (x^(4) + y^(4) + z^(2))/(xyz) ge sqrt(8)`
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