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 ENGLISH|Exercise All Questions|15 Videos
  • MATRICES

    RESONANCE DPP ENGLISH|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

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

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

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

For all positive numbers x,y,z the product ((1)/(x+y+z))((1)/(x)+(1)/(y)+(1)/(z))((1)/(xy+yz+zx))((1)/(xy)+(1)/(yz)+(1)/(zx)) equals

The value of {(x-y)^3+(y-z)^3+(z-x)^3}/{9(x-y)(y-z)(z-x)} (1) 0 (2) 1/9 (3) 1/3 (4) 1

If x, y, z are non-negative real numbers satisfying x+y+z=1 , then the minimum value of ((1)/(x)+1)((1)/(y)+1)((1)/(z)+1) , is

If x y+y z+x z=1 ,then prove that x/(1-x^2)+y/(1-y^2)+z/(1-z^2)=(4x y z)/((1-x^2)(1-y^2)(1-z^2)

If x y+y z+x z=1 ,then prove that x/(1-x^2)+y/(1-y^2)+z/(1-z^2)=(4x y z)/((1-x^2)(1-y^2)(1-z^2)

If x > y > z >0, then find the value of cot^(-1)(x y+1)/(x-y)+cot^(-1)(y z+1)/(y-z)+cot^(-1)(z x+1)/(z-x)

RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. Match the column Column I, Column II If x=3,t h e n(log)4(2(log)3(1...

    Text Solution

    |

  2. The positive integers p ,q and r all are prime if p^2-q^2=r , then pos...

    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 (a)only one solution (b) infi...

    Text Solution

    |

  6. The solution set of equation |2x+3|-|x-1| =6, is

    Text Solution

    |

  7. The number of integral solution of (x^(2)(3x-4)^(3)(x-2)^(4))/(In(2x-1...

    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 (a)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 a...

    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. Find tha value of the expression 2/log4(2000)^6+3/log5(2000)^6

    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))+..+log(3)(1+(1)/...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. If log(10)(x-1)3-3log(10)(x-3)=log(10)8,then log(x)625 has the value e...

    Text Solution

    |

  20. If log (10)xlog 15-a and log75-b, then log(75)45 is:

    Text Solution

    |