`(2+5omega +2 omega^2)^6=(2+2omega+5 omega^2)^6=729`

Explanation

`L.H.S.=(2+5omega+2omega^2)^6`
`=(2+2omega^2+5omega)^6={2(1+omega^2)+5omega}^6`
`=(-2omega+5omega)^6=(3omega)^6=729omega^6=729`
`"Again", (2+2omega+5omega^2)^6`
`={2(1+omega)+5omega^2}^6`
`=(-2omega^2+5omega^2)^6=(3omega^2)^6`
`=729omega^(12)=729`
`:.(2+5omega+2omega^2)^6=(2+2omega+5omega^2)^6=729`