InterviewSolution
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InterviewSolution
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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))` |
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Answer» `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))` |
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