Home
Class 12
MATHS
If x,y,z are different and Delta= {:|(x,...

If x,y,z are different and `Delta= {:|(x,x^2,1+x^3),(y,y^2,1+y^3),(z,z^2,1+z^3)|=0`, show that xyz=-1

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    MODERN PUBLICATION|Exercise EXERCISE|326 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise EXERCISE|588 Videos

  • EXCLUSIVELY FOR JEE(ADVANCED)

    MODERN PUBLICATION|Exercise EXERCISE|38 Videos

Similar Questions

Explore conceptually related problems

If x, y, z are all distinct and |(x,x^(2),1+x^(3)),(y,y^(2),1+y^(3)),(z,z^(2),1+z^(3))|=0 then value of x y z is :

Show that |(1,x^2,x^3),(1,y^2,y^3),(1,z^2,z^3)| = (x-y),(y-z)(z-x)(xy+yz+zx)

Prove that: {:|(1,x,x^3),(1,y,y^3),(1,z,z^3)| = (x-y)(y-z)(z-x)(x+y+z)

Using properties of determinants, prove that: |[x,x^2,1+px^3],[y,y^2,1+py^3],[z,z^2,1+pz^3]| = (1+pxyz)(x-y)(y-z)(z-x)

If x != y != z and |[[x,x^2,1+x^3],[y,y^2,1+y^3],[z,z^2,1+z^3]]|=0 then using properties of determinants, show that xyz= -1.

If xneynez and |[x,x^3,x^4-1],[y,y^3,y^4-1],[z,z^3,z^4-1]|=0 , then prove that : xyz(xy+yz+zx)=x+y+z

Prove the following identities : |{:(x,x^(2),x^(3)),(y,y^(2),y^(3)),(z,z^(2),z^(3)):}|=xyz(x-y)(y-z)(z-x) .

MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. If x,y,z are different and Delta= {:|(x,x^2,1+x^3),(y,y^2,1+y^3),(z,z^...

    Text Solution

    |

  2. Let A be a square matrix of order 3xx3, then prove that |kA|=k|A|.

    Text Solution

    |

  3. If any two rows (or columns) of a determinant are identical, the value...

    Text Solution

    |

  4. Answer in one word. {:|(3,1,6),(5,2,10),(7,4,14)|

    Text Solution

    |

  5. If A is a square matrix of order 3 and |3A| = k|A|, then write the val...

    Text Solution

    |

  6. Write the value of the following determinant abs{:(a-b, b-c, c-a),(b-c...

    Text Solution

    |

  7. Use properties of determinants ot evaluate: {:|(2,a,abc),(2,b,bca),(...

    Text Solution

    |

  8. Use properties of determinants ot evaluate: {:|(x+y,y+z,z+x),(z,x,y)...

    Text Solution

    |

  9. Evaluate |[102,18,36],[1,3,4],[17,3,6]|

    Text Solution

    |

  10. Use properties of determinants ot evaluate: {:|(2,3,1),(4,6,2),(1,3,...

    Text Solution

    |

  11. Use properties of determinants ot evaluate: {:|(2,3,5),(261,592,127)...

    Text Solution

    |

  12. Show that x=1 is a root of the equation: {:|(x+1,2x,-11),(2x,x+1,-4...

    Text Solution

    |

  13. If p,q,r ar in A.P. write the value of : {:|(x+1,x+2,x+2p),(x+2,x+3,...

    Text Solution

    |

  14. Without expanding, prove that the following determinant vanishes. |...

    Text Solution

    |

  15. Without actual expansion, prove that the following determinants vanish...

    Text Solution

    |

  16. Without actual expansion, prove that the following determinants vanish...

    Text Solution

    |

  17. Without actual expansion, prove that the following determinants vanish...

    Text Solution

    |

  18. Without actual expansion, prove that the following determinants vanish...

    Text Solution

    |

  19. Without actual expansion, prove that the following determinants vanish...

    Text Solution

    |

  20. Without expanding, prove that Delta = abs{:(x+y, y + z, z+ x),(z, x ,...

    Text Solution

    |

  21. Without expanding, prove that : |{:(1, bc, a(b+ c) ),(1, ca, b ( c+ a)...

    Text Solution

    |