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x+y+z=0 అయితే x^(3)+y^(3)+z^(3)=3xyz అని...

`x+y+z=0` అయితే `x^(3)+y^(3)+z^(3)=3xyz` అని నిరూపించండి.

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If x+y+z=0 show that x^(3)+y^(3)+z^(3)=3xyz .

(a) If x + y + z=0, show that x ^(3) + y ^(3) + z ^(3)= 3 xyz. (b) Show that (a-b) ^(3) + (b-c) ^(3) + (c-a)^(3) =3 (a-b) (b-c) (c-a)

If x+y+z=0, show that x^3 + y^3+z^3- 3xyz .

If u = log (x^(3) + y^(3) + z^(3) - 3xyz) , then (x + y + z)(u_(x) + u_(y) + u_(z)) is equal to

If 1 , omega , omega^(2) are the cube roots of unity, then prove that ( x + y + z) ( x + y omega + z omega^(2)) ( x + yomega^(2) + z omega) = x^(3) + y^(3) + z^(3) - 3xyz

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

11x y^2 z^3 // 55xyz = ___

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

Do the following Division 8x^(3)y^(3)z^(3) div 16 xyz

VGS PUBLICATION-BRILLIANT-POLYNOMIAL AND FACTORIISATION-EXERCISE
  1. Factorise : 27x^3+y^3+z^3-9xyz using identity.

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

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  3. x+y+z=0 అయితే x^(3)+y^(3)+z^(3)=3xyz అని నిరూపించండి.

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  4. Show that (a-b)^3+(b-c)^3+(c-a)^3=3(a-b)(b-c)(c-a)

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  5. Without actual calculating the cubes, find the value of the following ...

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  6. Without actual calculating the cubes, find the value of the following ...

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  7. Without actual calculating the cubes, find the value of the following....

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  8. Without actual calculating the cubes , find the value of each of the f...

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  9. Give possible expressions for the length and breadth of the rectangle ...

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  10. Give possible expressions for the length and breadth of the rectangle ...

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  11. Whar are tge possible expression for the dimension the cuboids whose v...

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  12. Whar are tge possible expression for the dimension the cuboids whose v...

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  13. If 2 (a ^(12) + b ^(2)) = (a+b)^(2), then show that a =b

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  14. Write a binomial and trinomial in variable x.

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  15. Write the general form of a polyno mial in one variable x of degree n.

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  16. If P(x) =  X^2+ 5x + 4, find p(1) and P(-1).

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  17. Define zero of a polynomial.

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  18. Find the zero of the polynomial p(x) = 2x+5.

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  19. Find a zero of the polynomial p(X) = 3x - 1.

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  20. x ^(2) +1 has no real zeroes. Why ?

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