The minimum value of `P=bcx +cay +abz`, when `xyz=abc`, is

Explanation

To find the minimum value of
`bcx+cay+abz`,
write, `xyz=abc`
or `(bcx)(cay)(abz)=a^(3)b^(3)c^(3)=k " " [ " constant "]`
Here, `n=3`
Hence, minimum value of `bcx+cay+abz=n(k)^((1)/(n))`
`=3(a^(3)b^(3)c^(3))^((1)/(3))=3abc`.