Home
Class 11
MATHS
If a,b,c be in H.P prove that (1/a+1/b-1...

If a,b,c be in H.P prove that `(1/a+1/b-1/c)(1/b+1/c-1/a)=4/(ac)-3/b^2`

A

`2/(bc)-1/b^2`

B

`1/4(3/c^2+2/(ca)-1/a^2)`

C

`3/b^2-2/(ab)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
1,2&3
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    PATHFINDER|Exercise QUESTION BANK|41 Videos

  • QUADRATIC EQUATION

    PATHFINDER|Exercise QUESTION BANK|19 Videos

Similar Questions

Explore conceptually related problems

If a, b, c are in H.P., prove that, (1)/(bc), (1)/(ca), (1)/(ab) are in H.P.

If a^2, b^2, c^2 are in A.P , then prove that 1/(b+c), 1/(c+a),1/(a+b) are in A.P

If (b-c)^(2), (c-a)^(2), (a-b)^(2) are in A.P. then prove that, (1)/(b-c), (1)/(c-a), (1)/(a-b) are also in A.P.

If a,b,c are in HP and agtcgt0, then 1/(b-c)-1/(a-b) .

If a^(2), b^(2), c^(2) are in A.P., prove that (1)/(b+c), (1)/(c+a), (1)/(a+b) are also in A.P.

If (b-c)^2,(c-a)^2,(a-b)^2 are in A.P., then prove that 1/(b-c),1/(c-a),1/(a-b) are also in A.P.

If a ,b ,c in R+ form an A.P., then prove that a+1//(b c),b+(1//a c),c+1//(a b) are also in A.P.

If a ,b ,c ,d are in G.P., then prove that (a^3+b^3)^(-1),(b^3+c^3)^(-1),(c^3+d^3)^(-1) are also in G.P.

If 2^a=3^b=6^(-c) , then prove that (1)/(a)+(1)/(b)+(1)/(c )=0 .

If a, b, c are in A.P. then show that, a((1)/(b)+(1)/(c )), b((1)/(c )+(1)/(a)) and c((1)/(a)+(1)/(b)) are also in A.P.

PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. A geometric progression of real number is such that the sum of its fir...

    Text Solution

    |

  2. If the first and the (2n-1)^th term of an A.P,G.P anf H.P are equal an...

    Text Solution

    |

  3. If a,b,c be in H.P prove that (1/a+1/b-1/c)(1/b+1/c-1/a)=4/(ac)-3/b^2

    Text Solution

    |

  4. Which one of the following statements is correct ?

    Text Solution

    |

  5. Let sinalpha,cosalpha, be the roots of the equation x^2-bx+c=0. Then w...

    Text Solution

    |

  6. Which one of the following statements is correct ?

    Text Solution

    |

  7. The sum V1+V2+.....Vn is

    Text Solution

    |

  8. Tr is always

    Text Solution

    |

  9. Which one of the following statements is correct ?

    Text Solution

    |

  10. Match List-I with List-II

    Text Solution

    |

  11. The roots of equation x^2+2(a-3)x+9=0 lie between -6 and 1 and 2 , h1,...

    Text Solution

    |

  12. If a,b,c ,d are distinct integer in AP such that d=a^2+b^2+c^2, then a...

    Text Solution

    |

  13. If log2(a+b)+log2(c+d)ge4 . Then the minimum value of the expression a...

    Text Solution

    |

  14. Let a1,a2,a3,.......a11 be real number satisfying a1=15,27-2a2gt0 anda...

    Text Solution

    |

  15. The interior angles of a polygon are in arithmetic progression. The sm...

    Text Solution

    |

  16. Find the sum of the first n terms of the series 1^3+3.2^2+3^3+3.4^2+5^...

    Text Solution

    |

  17. Find the sum of the first n terms of the series 1^3+3.2^2+3^3+3.4^2+5^...

    Text Solution

    |

  18. Does there exist a GP containing 27,8 and 12 as three of its terms ? I...

    Text Solution

    |

  19. The sum of the squares of three distinct real numbers, which are in GP...

    Text Solution

    |

  20. Prove that the three successive terms of a GP will form the sides of ...

    Text Solution

    |