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x+y+z=0 Show that x^(3)+y^(2)+z^(3)=3xyz...

`x+y+z=0` Show that `x^(3)+y^(2)+z^(3)=3xyz`

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If alpha,beta are complex cube roots of unity and x=a+b , y=aalpha+bbeta , z=abeta+balpha , then the value of (x^(3)+y^(3)+z^(3))/(xyz) is:

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Factorise 27 x ^(3) + y ^(3) + z ^(3)-9 xyz using identitiy.

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Verify that x ^(3) + y ^(3) + z ^(3) - 3xyz =1/2 (x + y + z) [(x-y)^(2) + (y-z) ^(2) + (z-x) ^(2) ]

If x_(1) = 3y_(1) + 2y_(2) -y_(3), " " y_(1)=z_(1) - z_(2) + z_(3) x_(2) = -y_(1) + 4y_(2) + 5y_(3), y_(2)= z_(2) + 3z_(3) x_( 3)= y_(1) -y_(2) + 3y_(3)," " y_(3) = 2z_(1) + z_(2) express x_(1), x_(2), x_(3) in terms of z_(1) ,z_(2),z_(3) .

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SUBHASH PUBLICATION-POLYNOMIALS-EXERCISE 4.5
  1. Factorise : - 4x^(2) +9y^(2)+16z^(2)+12xy-24yz-16xz

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  2. Factorise : - 2x^(2)+y^(2)+8z^(2)-2sqrt(2)xy+4sqrt(2)yz-8xz

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  3. Write the following cubes in expanded form. (2x+1)^(3)

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  4. Write the following cubes in expanded form. (2a-3b)^(3)

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  5. Write the following cubes in expanded form. [3/2x+1]^(3)

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  6. Write the following cubes in expanded form. (x-2/3y)^(3)

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  7. Evaluate using the suitable identity. (99)^(3)

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  8. Evaluate using the suitable identity. (102)^(3)

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  9. Evaluate using the suitable identity. (998)^(3)

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  10. Factorise each of the following . 8a^(3)+b^(3)+12a^(2)b+6ab^(2)

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  11. Factorise each of the following . 8a^(3)-b^(3)-12a^(2)b+6ab^(2)

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  12. Factorise each of the following . 27-125a^(3)-135a+225a^(2)

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  13. Factorise each of the following . 64a^(3)-27b^(3)-144a^(2)b + 108ab^...

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  14. x+y+z=0 Show that x^(3)+y^(2)+z^(3)=3xyz

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  15. Without actually calculating the cubes , find the value of the followi...

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  16. Without actually calculating the cubes , find the value of the followi...

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  17. Give passible expressions for the length and breadth of each of the fo...

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  18. Give passible expressions for the length and breadth of each of the fo...

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  19. What are the possible expressions for the dimensions of the cuboids wh...

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  20. What are the possible expressions for the dimensions of the cuboids wh...

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