Ta có : `2^x+4^y+16^z=2^x+2^{2y}+2^{4z}=34` `(x,y,z>=0)`

Tổng quát : `(2^a-1)(2^b-1)>=0` `(` Vì `a,b>=0)`

`<=>2^a 2^b-2^a -2^b+1>=0`

`<=>2^{a+b}+1>=2^a+2^b`

Áp dụng : `2^{x+2y}+1>=2^x+2^{2y}`

`<=>2^{x+2y}+1+2^{4z}>=2^x+2^{2y}+2^{4z}=34`

`<=>2^{x+2y}+2^{4z}>=33`

Lại có `2^{(x+2y)+4z}+1>=2^{x+2y}+2^{4z}>=33`

`<=>2^{x+2y+4z}>=32=2^5<=>x+2y+4z>=5`

Suy ra : ` P=x/4+y/2+z>=5/4`

Vậy `P_{M i n}=5/4`