Home
Class 9
MATHS
if x+y+z=0,then Prove that (xyz)/((x+y...

if x+y+z=0,then Prove that
`(xyz)/((x+y)(y+z)(z+x))=-1 where(x!=-y,y!=-z,z!=-x)`

Promotional Banner

Topper's Solved these Questions

  • HARDER PRODUCT AND FACTORISATION

    KALYANI PUBLICATION|Exercise EXERCISE|148 Videos

  • GEOMETRY

    KALYANI PUBLICATION|Exercise EXERCISE|10 Videos

  • INEQUALITIES AND INEQUATIONS

    KALYANI PUBLICATION|Exercise EXERCISE|126 Videos

Similar Questions

Explore conceptually related problems

Prove that (x-y)^3+(y-z)^3+(z-x)^3=3(x-y)(y-z)(z-x)

If x, y, z,w in are in G.P., prove that (xy-wz)/(y^2-z^2)=(x+z)/y .

Prove that (3x-2y)^3+(y-2z)^3+(y+2z-3x)^3=3(3x-2y)(y-2z)(y+2z-3x)

Prove that (3x-2y)^3+(y+2z)^3+(y-2z-3x)^3=3(3x-2y)(y+2z)(y-2z-3x)

Prove that 4x^2(y-z)+y^2(2x-z)+z^2(2x+y)-4xyz = (2x+y)(y-z)(2x-z)

Prove that |(y+z, x,y),(z+x, z, x),(x+y, y, z)| = (x+y+z)(x-z)^(2) .

If x^(1/3)+y^(1/3)+z^(1/3)=0 , then prove that (x+y+z)^3=27xyz

If s= x+y+z , then prove that s^3+x^3+y^3+z^3-(s-x)^3-(s-y)^3-(s-z)^3=6xyz

If x = 10 , y = 64, and z = 2, then prove that (x+y+z)^3 = 438976

Prove that (x+2y+3z)^3-x^3-8y^3-27z^3=3(2y+3z)(x+3z)(x+2y)

KALYANI PUBLICATION-HARDER PRODUCT AND FACTORISATION -EXERCISE
  1. Prove that (a+b+c)^3-(a^3+b^3+c^3)=3(b+c)(c+a)(a+b)

    Text Solution

    |

  2. Prove that (a-b)^3+(b-c)^3+(c-a)^3=3(a-b)(b-c)(c-a)

    Text Solution

    |

  3. if x+y+z=0,then Prove that (xyz)/((x+y)(y+z)(z+x))=-1 where(x!=-y,y!...

    Text Solution

    |

  4. Prove that If a=2, b=3, c=5. Then prove that 2b^2c^2+2c^2a^2+2a^2b...

    Text Solution

    |

  5. Prove that If 3x+2y=-1, then prove that 81x^4+16y^4+1-72x^2y^2-18x...

    Text Solution

    |

  6. If x-y=7and xy=9, then find the value of (x^2+y^2)

    Text Solution

    |

  7. Prove that 4x^2(y-z)+y^2(2x-z)+z^2(2x+y)-4xyz = (2x+y)(y-z)(2x-z)

    Text Solution

    |

  8. Prove that (x-a)^2/((a-b)(a-c))+(x-b)^2/((b-a)(b-c))+(x-c)^2/((c-a)(...

    Text Solution

    |

  9. Prove that 1/(a(a-b)(a-c))+1/(b(b-c)(b-a))+1/(c(c-a)(c-b))=1/(abc)

    Text Solution

    |

  10. Prove that a/(bc(a-b)(a-c))+b/(ca(b-c)(b-a))+c/(ab(c-a)(c-a))=1/(abc...

    Text Solution

    |

  11. Prove that 2(s-a)(s-b)(s-c)+a(s-b)(s-c)+b(s-c)(s-a)+c(s-a)(s-b)=abc ...

    Text Solution

    |

  12. Factorise a^3-b^3+1+3ab

    Text Solution

    |

  13. If a + b + c = 0, then prove that 1/(2a^2+bc)+1/(2b^2+ca)+1/(2c^2+a...

    Text Solution

    |

  14. If a^2 + b^2 + c^2 -ab-bc-ca = 0, then prove that a=b=c

    Text Solution

    |

  15. If a + b + c = 0, then prove that (a+b)^2/(ab) + (b+c)^2/(bc) + (c+...

    Text Solution

    |

  16. If a + b + c = 0, then prove that (2a^2)/(a^2-b^2-c^2)+(2b^2)/(b^2-...

    Text Solution

    |

  17. If a + b + c = 0, then prove that (a^2+b^2+c^2)/(a^3+b^3+c^3)+2/3(1...

    Text Solution

    |

  18. If a+b=c then prove that 1/(b^2+c^2-a^2)+1/(c^2+a^2-b^2)+1/(a^2+b^2...

    Text Solution

    |

  19. If a+b+c=0, then prove that a(c+a)(a+b)=b(a+b)(b+c)=c(a+c)(b+c)=abc

    Text Solution

    |

  20. If a+b+c=0, then prove that a(b+c)^2+b(c+a)^2+c(a+b)^2=3abc

    Text Solution

    |