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If x+y+z=1,\ x y+y z+z x=-1\ \ a n d\ x ...

If `x+y+z=1,\ x y+y z+z x=-1\ \ a n d\ x y z=-1,` find the value of `x^3+y^3+z^3`

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To find the value of \( x^3 + y^3 + z^3 \) given the equations: 1. \( x + y + z = 1 \) 2. \( xy + yz + zx = -1 \) 3. \( xyz = -1 \) We can use the identity: ...
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RD SHARMA-ALGEBRAIC IDENTITIES-All Questions
  1. Without actually calculating the cub: (-12)^3+7^3+5^3

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  2. Without actually calculating the cub: (28)^3+\ (-15)^3+\ (-13)^3

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  3. If x+y+z=1,\ x y+y z+z x=-1\ \ a n d\ x y z=-1, find the value of x^3+...

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  4. Simplify: ((a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3)/((a-b)^3+(b-c)^3+(c-a...

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  5. Find the product: (3x+2y+2z)\ \ (9x^2+4y^2+\ 4\ z^2-\ 6\ x y-4\ y z-6z...

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  6. Find the product: (4x-3y+2z)\ (16 x^2+9y^2+4z^2+12 x y+6y z-8z x)

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  7. Find the product: (2a-3b-2c)(4\ a^2+\ 9\ b^2+\ 4\ c^2+\ 6\ a b-6\ b c+...

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  8. Find the product: (3x-4y+5z)\ (9x^2+16 y^2+25 z^2+12 x y-15 z x+20 y z...

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  9. If x+y+z=8\ \ a n d\ \ \ x y+y z+z x=20 , find the value of x^3+y^3+z^...

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  10. If a+b+c=9\ \ \ a n d\ \ \ a b+b c+c a=26 , find the value of a^3+b^3+...

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  11. If a+b+c=9 and a^2+b^2+c^2=35 , find the value of a^3+b^3+c^3-3a b c

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  12. Evaluate: 25^3-75^3+50^3

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  13. Evaluate: 48^3-30^3-18^3

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  14. Evaluate: (1/2)^3+\ (1/3)^3-\ \ (5/6)^3

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  15. Evaluate: (0. 2)^3-\ (0. 3)^3+\ (0. 1)^3

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  16. If x+1/x=3, then find the value of x^2+1/x^2

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  17. If x+1/x=3, then the value of x^6+1/x^6is.

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  18. If a+b=7\ \ a n d\ \ a b=12 , find the value of a^2+b^2

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  19. If a-b=5 and a b=12 , find the value of a^2+b^2

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  20. If x-1/x=1/2 , then write the value of 4x^2+4/(x^2)

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