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If x+y+z=1,x y+y z+z x=-1 and x y z=-1, ...

If `x+y+z=1,x y+y z+z x=-1` and `x y z=-1,` find the value of `x^3+y^3+z^3dot`

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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. If a+b=7 and a b=12 , find the value of (a^2-a b+b^2)

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  2. If x^2+1/(x^2)=83. find the value of x^3-1//x^3

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

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  4. Find the following products: (i) (0. 9 x+0. 7 y)(0. 81 x^2-0. 63 x y+0...

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  5. If a+b+c=15 and a^2+b^2+c^2=83 , find the value of a^3+b^3+c^3-3abc

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  6. Without actually calculating the cubes. Find the value of each of t...

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  7. Ifa +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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  8. If x-1/x=3+2sqrt(2) , find the value of x^3-1/(x^3)

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  9. If x+y=12 and x y=32 , find the value of x^2+y^2dot

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  10. If 3x+2y=12 and x y=6, find the value of 9x^2+4y^2 (3x+2y)^2=9x^2+4y...

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  11. If x+1/x=6 , find x^2+1/(x^2) (ii) x^4+1/(x^4) (x+1//x)^2=6 x^2+1/...

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  12. If x^2+1/(x^2)=27 , find the values of each of the following: x+1/x (...

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  13. Find the products: (i) (2x+3y)(2x-3y) (ii)(x-1)(x+1)(x^2+1)(x^4+1)

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  14. Without calculating the actual cube find the value of (-12)^3+7^3+5^...

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  15. Expand each of the following: (i)(3x+4y)^2 (ii) (3x-4y)^2

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  16. If x-1/x=3, find the value of x^3-1/(x^3)

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  17. If 2x+3y=13 and x y=6, find the value of 8x^3+27 y^3

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  18. If a+b=10 and a^2+b^2=58 , find the value of a^3+b^3

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  19. If x+1/x=7, find the value of x^3+1/(x^3)

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  20. Simplify each of the following expressions: (i) (x+y+z)^2+(x+y/2+z/3)...

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