Home
Class 12
MATHS
If |(x, x^2, x^3 +1), (y, y^2, y^3+1), (...

If `|(x, x^2, x^3 +1), (y, y^2, y^3+1), (z, z^2, z^3+1)|` = 0 and x ,y and z are not equal to any other, prove that, xyz = -1

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • JEE MAIN

    JEE MAINS PREVIOUS YEAR ENGLISH|Exercise MATH|21 Videos

  • LIMITS AND DERIVATIVES

    JEE MAINS PREVIOUS YEAR ENGLISH|Exercise All Questions|5 Videos

Similar Questions

Explore conceptually related problems

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

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 prove that x y z=-1 .

If xneynez" and " |{:(x,x^(2),1+x^(3)),(y,y^(2),1+y^(3)),(z,z^(2),1+z^(3)):}|=0, then xyz =

If x, y, z are different and Delta=|xx^2 1+x^3y y^2 1+y^3z z^2 1+z^3|=0 , then

If x!=y!=za n d|[x,x^2, 1+x^3],[y ,y^2 ,1+y^3],[z, z^2, 1+z^3]|=0, then the value of x y z is a. 1 b. 2 c. -1 d. 2

If |(x^k,x^(k+2),x^(k+3)), (y^k,y^(k+2),y^(k+3)), (z^k,z^(k+2),z^(k+3))|=(x-y)(y-z)(z-x){1/x+1/y+1/z} then k=

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 then show that 1+xyz=0

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 then show that 1+xyz=0

If cos^-1 x+cos^-1 y+cos^-1 z=pi and x+y+z= 3/2, then prove that x=y=z

Prove that : Det[[x,x^2,x^3],[y,y^2,y^3],[z,z^2,z^3]]=xyz(x-y)(y-z)(z-x)

JEE MAINS PREVIOUS YEAR ENGLISH-JEE MAINS-All Questions
  1. If x=9 is the chord of contact of the hyperbola x^2-y^2=9 then the equ...

    Text Solution

    |

  2. Find the value of log tan1^0logtan2^0...........logtan89^0

    Text Solution

    |

  3. If |(x, x^2, x^3 +1), (y, y^2, y^3+1), (z, z^2, z^3+1)| = 0 and x ,y a...

    Text Solution

    |

  4. If z lies on the circle |z-1|=1, then (z-2)/z is

    Text Solution

    |

  5. Find the coordinates of a point on the (x-1)/2=(y+1)/(-3)=z atg a d...

    Text Solution

    |

  6. The point of intersection of two tangents to the hyperbola (x^(2))/(a^...

    Text Solution

    |

  7. prove that int1/(x(x^4+1))dx=1/4log(x^4/(x^4+1))+c

    Text Solution

    |

  8. If (lim)(xvec0)[cot(pi/4+x)]^(1//x)=A e^2 then the value of A is: e^2 ...

    Text Solution

    |

  9. A man is known to speak truth 3 out of 4 times. He throws a die and re...

    Text Solution

    |

  10. If the tangent at (1,1) on y^2=x(2-x)^2 meets the curve again at P , t...

    Text Solution

    |

  11. The degree of het differential equation sqrt(1+((dy)/(dx))^2)=x^2 is (...

    Text Solution

    |

  12. Let f: Rvec[3,5] be a differentiable function such that (lim)(xvecoo)f...

    Text Solution

    |

  13. If a triangle is inscribed in a rectangular hyperbola, it’s orhtocente...

    Text Solution

    |

  14. Let f:[0,5] to [-1,5], where f(x)={x^2-1,0 <= x < 2 , 1/3(19-2x), 2 < ...

    Text Solution

    |

  15. Area bounded by the curve y=sqrt(sin[x]+[sinx]),(w h e r e[dot] is gre...

    Text Solution

    |

  16. Let vec r=( vec axx vec b)sinx+( vec bxx vec c)cosy+2( vec cxx vec a),...

    Text Solution

    |

  17. Let y=f(x) be an even function. If f^(prime)(2)=-sqrt(3) , then the in...

    Text Solution

    |

  18. If positive numbers a ,b ,c are in H.P., then equation x^2-k x+2b^(10...

    Text Solution

    |

  19. The digit in the unit place of the number (183)!+3^183 is

    Text Solution

    |

  20. The equation of diameter of a circle passing through origin is x+y=1 a...

    Text Solution

    |