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

  • PUNJAB BOARD-MATHEMATICS 2018

    OMEGA PUBLICATION|Exercise SERIES -C|19 Videos

  • PUNJAB BOARD-MATHEMATICS 2018

    OMEGA PUBLICATION|Exercise SERIES -C|19 Videos

  • PUNJAB BOARD - MATHEMATICS 2019

    OMEGA PUBLICATION|Exercise SERIES-C|58 Videos

  • RELATIONS AND FUNCTIONS

    OMEGA PUBLICATION|Exercise MULTIPLE CHOICE QUESTIONS (MCQs) |20 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) .

OMEGA PUBLICATION-PUNJAB BOARD-MATHEMATICS 2018-SERIES -B
  1. Using differentials find approximate value of (0.37)^(1/2)

    Text Solution

    |

  2. Evaluate int(x^(2)-1)/(x^(4)+1)dx

    Text Solution

    |

  3. Evaluate int(dx)/(x^3-1)

    Text Solution

    |

  4. If veca=2hati-3hatj+4hatk and vecb=5hati+hatj-hatk represents sides of...

    Text Solution

    |

  5. Two cards are drawn (without replacement) from a well shuffled deck of...

    Text Solution

    |

  6. Find the particular solution of differential equations : [x sin^2(y/x)...

    Text Solution

    |

  7. Find the particular solution of differential equation : tan x dy/dx+y=...

    Text Solution

    |

  8. Prove that function f: RrarrR, f(x)=(3x-2)/7 in one-one and onto. Also...

    Text Solution

    |

  9. Exress [(2,5,-1),(3,1,5),(7,6,9)] as a sum of a symmetric matrix and a...

    Text Solution

    |

  10. If x,y,z are different and Delta= {:|(x,x^2,1+x^3),(y,y^2,1+y^3),(z,z^...

    Text Solution

    |

  11. Prove that : sin^(-1)(5/13)+cos^(-1)(4/5)=1/2sin^(-1)(3696/4225).

    Text Solution

    |

  12. Find the area of the region bounded by the elipse (x^(2))/9+(y^(2))/4=...

    Text Solution

    |

  13. A window is in the form of rectangle surmounted by a semi-circular ope...

    Text Solution

    |

  14. Prove that volume of largest cone, which can be inscribed in a sphere,...

    Text Solution

    |

  15. Maximise and minimize Z=15x+30y subject to the constraints x+y le 8 ...

    Text Solution

    |

  16. Maximum Z=4x+3y-7 subject to the constraints x+yle10,x+yge3,xle8,yle...

    Text Solution

    |

  17. Solve the following system of linear equations by matrix method : x - ...

    Text Solution

    |

  18. Using elementary transformations find the inverse of [[2,4,1],[1,2,3],...

    Text Solution

    |

  19. Find the distance between the point (2, 3, - 1) and foot of perpendicu...

    Text Solution

    |

  20. Find the equation of plane passing from the point A(2,-1,1),B(4,3,2) a...

    Text Solution

    |