यदि `x=a+b,y=aomega+bomega^(2),z=aomega^(2)+bomega`, तो सिद्ध कीजिए कि -
`x^(3)+y^(3)+z^(3)=3(a^(3)+b^(3))`

Explanation

`x+y+z=(a+b)+(aomega+bomega^(2))+(aomega^(2)+bomega)`
`=(1+omega+omega^(2))+b(1+omega+omega^(2))=axx0+bxx0=0` . . . (i)
`" "(because1+omega+omega^(2)=0)`
हम जानते है कि
`x^(3)+y^(3)+z^(3)-3xyz=(x+y+z)(x^(2)+y^(2)+z^(2)-xy-yz-zx)`
`=0xx(X^(2)+y^(2)+z^(2)-xy-yz-zx)=0" "` (समीकरण (i) से)
`:." "x^(3)+y^(3)+z^(3)=3xyz=3(a^(3)+b^(3))" "(becausexyz=a^(3)+b^(3))`