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If x=a+b,y=aomega+bomega^2 nd z=omega^2+...

If `x=a+b,y=aomega+bomega^2 nd z=omega^2+bomega`, prove that `x^3+y^3+z^3=3(a^3+b^3)`

A

`x pm y + z ne 0`

B

` x^(2) + y^(2) + z^(2) = a^(2) + b^(2)`

C

`x^(3) + y^(3) + z^(3) = 3 (a^(3) + b^(3))`

D

`xyz = 2 (a^(3) + b^(3))`

Text Solution

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The correct Answer is:
C
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ML KHANNA-COMPLEX NUMBERS -Problem Set (2) (M.C.Q)
  1. If omega is a cube root of unity but not equal to 1, then minimum valu...

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  2. If x=a+b,y=aomega+bomega^2 nd z=omega^2+bomega, prove that x^3+y^3+z^3...

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  3. If x=a+b,y=aomega+bomega^2 nd z=omega^2+bomega, prove that x^3+y^3+z^3...

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  4. If omega pm 1 is a cube root of unity, the value of (a + b omega + c o...

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  5. If alpha, beta, gamma are the cube roots of p, p lt 0 then for an...

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  6. If alpha , beta , gamma are cube roots of p lt 0, then for any x , y,...

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  7. The value |(1 + omega,omega^(2),-omega),(1 + omega^(2),omega,-omega^(...

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  8. If omega is imaginary cube root of unity then Delta = |(1,1 + i ...

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  9. |(6i,-3i,1),(4,3i,-1),(20,3,i)| = x + iy then (x,y) is

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  10. If alpha is a root of x^(4) - 1 = 0 with negative principal argum...

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  11. If omega be complex cube root of unity satisfying the equation (1 )/...

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  12. If 1 , omega, omega^(2), . . . omega^(n - 1) are the n, nth roots of ...

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  13. If alpha is an n th root of unity other than unity itself, then the ...

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  14. If omega is an imaginary fifth root of unity, then find the value of l...

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  15. The product of all n^(th) root of unity is always

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  16. The roots of the cubic equation (z + ab)^(3) = a ^(3) , a ne 0 represe...

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  17. If If 1, alpha(1), alpha(2), alpha(3) , . . . alpha(n - 1) are the n...

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  18. If beta ne 1 be any nth root of unity, then 1 + 3 beta + 5 beta ^...

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  19. If 1,alpha,alpha^(2),……….,alpha^(n-1) are n^(th) root of unity, the va...

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  20. If p is a multiple of n , then the sum of pth powers of nth roots of u...

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