Home
Class 9
MATHS
If x+y+z=0show that x^3+y^3+z^3=3x y z....

If `x+y+z=0`show that `x^3+y^3+z^3=3x y z`.

Promotional Banner

Topper's Solved these Questions

  • POLYNOMIALS

    NAGEEN PRAKASHAN|Exercise Revision Exercise (very Short Answer Questions)|10 Videos

  • POLYNOMIALS

    NAGEEN PRAKASHAN|Exercise Revision Exercise (short Answer Questions)|16 Videos

  • POLYNOMIALS

    NAGEEN PRAKASHAN|Exercise Exercise 2d|5 Videos

  • NUMBER SYSTEM

    NAGEEN PRAKASHAN|Exercise Revision Exercise (short Answer Questions)|10 Videos

  • PROBABILITY

    NAGEEN PRAKASHAN|Exercise Revision Exercise (very Short Answer /short Answer Questions)|10 Videos

Similar Questions

Explore conceptually related problems

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

If x+y+z=0 then x^3+y^3+z^3+3xyz equal to

Show that : |x y z x^2y^2z^2x^3y^3z^3|=x y z(x-y)(y-z)(z-x)dot

(i) Factorize the experssions 8a^(6)+5a^3+1 (ii) show that (x-y)^3+(z-x)^3+(z-x)^3=3(x-y)(y-z)(z-x)

If x+y+z=xyz , show that : (3x-x^3)/(1-3x^2) + (3y-y^3)/(1-3y^2) + (3z-z^3)/(1-3z^2) = (3x-x^3)/(1-3x^2) . (3y-y^3)/(1-3y^2) . (3z-z^3)/(1-3z^2)

If x + y + z = 0 , then ( x + y - z)^(3) + ( y + z - x)^(3) + (z + x - y) ^(3) = k (xyz) , where k is equal to :

NAGEEN PRAKASHAN-POLYNOMIALS-Exercise 2 E
  1. Evaluate without multiplying directly : (i) 33xx27 " " (ii) 103xx9...

    Text Solution

    |

  2. Expand : (i) (3a-5b)^(2) " " (ii) (a+(1)/(a))^(2) " " (iii) (2x-(...

    Text Solution

    |

  3. Expand : (i) (a+b-c)^(2) " " (ii) (a-2b-5c)^(2) " " (iii) (3a-2b...

    Text Solution

    |

  4. Evaluate using formula : (i) (188)^(2) " " (ii) (9.4)^(2) " " (i...

    Text Solution

    |

  5. (i) If a^(2)+b^(2)+c^(2)=20 " and" a+b+c=0, " find " ab+bc+ac. (ii) ...

    Text Solution

    |

  6. Expand : (i) (2x+3y)^(3) " " (ii) (5y-3x)^(3) " " (iii) (2a+3b)...

    Text Solution

    |

  7. Evaluate (2x-3y+5)^(3).

    Text Solution

    |

  8. If a+2b=5, then show that a^(3)+8b^(3)+30ab=125.

    Text Solution

    |

  9. If 2x-3y=10 and xy=16, find the value of 8x^(3)-27y^(3).

    Text Solution

    |

  10. Evaluate : (i) (98)^(3) " " (ii) (598)^(3) " " (iii) (1003)^(3)

    Text Solution

    |

  11. Factorise : (i) 4a^(2)+9b^(2)+16c^(2)+12ab-24bc-16ca (ii) (4)/(9)x...

    Text Solution

    |

  12. Verify : (i) x^(3)+y^(3)=(x+y)(x^(2)-xy+y^(2)) " " (ii) x^(3)-y^(...

    Text Solution

    |

  13. Factorise : (i) 9a^(3)-27b^(3) " " (ii) a^(3)-343 " " (iii) a^(...

    Text Solution

    |

  14. Find the product : (i) (x+3)(x^(2)-3x+9) " " (ii) (7+5b)(49-35b+2...

    Text Solution

    |

  15. Factorise : (i) a^(3)+27b^(3)+8c^(3)-18abc " " (ii) 2sqrt(2)a^(3)...

    Text Solution

    |

  16. Find the product : (i) (a+2b+4c)(a^(2)+4b^(2)+16c^(2)-2ab-8bc-4ca) ...

    Text Solution

    |

  17. Factorise : (i) (x-y)^(3)+(y-z)^(3)+(z-x)^(3) (ii) (x-2y)^(3)+(2y-...

    Text Solution

    |

  18. Without actually calculating the cube find the value of the following ...

    Text Solution

    |

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

    Text Solution

    |

  20. If x+y+z=0show that x^3+y^3+z^3=3x y z.

    Text Solution

    |