Home
Class 12
MATHS
If x , y , z are all different real numb...

If `x , y , z` are all different real numbers, then `1/((x-y)^2)+1/((y-z)^2)+1/((z-x)^2)=(1/(x-y)+1/(y-z)+1/(z-x))^2`

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP|Exercise All Questions|15 Videos
  • MATRICES

    RESONANCE DPP|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

If x,y,z are all different real numbers,then prove that (1)/((x-y)^(2))+(1)/((y-z)^(2))+(1)/((z-x)^(2))=((1)/(x-z)+(1)/(y-z)+(1)/(z-x))^(2)

If x,y,z are distinct real numbers then the value of ((1)/(x-y))^(2)+((1)/(y-z))^(2)+((1)/(z-x))^(2) is

If x,y,z are positive real numbers show that: sqrt(x^(-1)y)*sqrt(y^(-1)z)*sqrt(z^(-1)x)=1

(2-3x)/(x)+(2-3y)/(y)+(2-3z)/(z)=0 then (1)/(x)+(1)/(y)+(1)/(z)=

If xy + yz + zx = 1 , show that x/(1-x^(2)) +y/(1-y^(2)) + z/(1-z^(2))= 4xyz/((1-x^(2))(1-y^(2)) (1-z^(2)))

Prove that : =2|{:(1,1,1),(x,y,rz),(x^(2),y^(2),z^(2)):}|=(x-y)(y-z)(z-x)

If xy + yz + zx = 1 , show that x/(1-x^(2)) +y/(1-y^(2)) + z/(1-z^(2))= (4xyz)/((1-x^(2))(1-y^(2)) (1-z^(2)))

RESONANCE DPP-JEE MAINS-All Questions
  1. If alpha&beta are the roots of the quadratic equation a x^2+b x+c=0 ...

    Text Solution

    |

  2. The positive integers p ,q and r , then possible value of r is 3 (b) ...

    Text Solution

    |

  3. If x , y , z are all different real numbers, then 1/((x-y)^2)+1/((y-z)...

    Text Solution

    |

  4. Solution set of the inequation, (x^2-5x+6)/(x^2+x+1)<0 is x in (-oo,2)...

    Text Solution

    |

  5. The equation x-8/(|x-3|)=3-8/(|x-3|) has only one solution (b) infinit...

    Text Solution

    |

  6. The solution set of the equation |2x+3|-|x-1|=6, is x in (-10 ,2) (b)...

    Text Solution

    |

  7. The number of positive integral solutions of, (x^2(3x-4)^3(x-2)^4)/((x...

    Text Solution

    |

  8. If A+B+C=0 , then the value of sin^2A+cosC(cosAcosB-cosC)+cosB(cosAcos...

    Text Solution

    |

  9. If x=3-sqrt(8), then x^3+1/(x^3) is equal to 6 (b) 198 (c) 6sqrt(2)...

    Text Solution

    |

  10. If Pa n dQ are sum and product respectively of all real values of x sa...

    Text Solution

    |

  11. A 3-digit number has, from left to right, the digits, a, b and c with ...

    Text Solution

    |

  12. If A , B , C are three real numbers and p=[A+b+C] and q=[A]+[B]+[C]dot...

    Text Solution

    |

  13. Value of [2/((log)4(2000)^6)+3/((log)5(2000)^6)]i s 4^(1/3). 5^(1/2)...

    Text Solution

    |

  14. If b^2>4a c then roots of equation a x^4+b x^2+c=0 are all real and di...

    Text Solution

    |

  15. If a x^2+b x=6=0 does not have distinct real roots, then find the leas...

    Text Solution

    |

  16. (log)3(1+1/3)+(log)3(1+1/4)+(log)3(1+1/5)+ddot+(log)3(1+1/(242)) when...

    Text Solution

    |

  17. If [x]=[pi] , where [.] denotes greatest integer function, then x in (...

    Text Solution

    |

  18. The number of real solutions of equation x^((log)x2)+x^2=3x is 2 (b) 1...

    Text Solution

    |

  19. If (log)(10)(x-1)^3-3(log)(10)8(x-3)=(log)(10)8, then (log)x 625 has t...

    Text Solution

    |

  20. If log15=a and log75=b , then (log)(75)45 is: (3b-a)/a (b) (b-3a)/a ...

    Text Solution

    |