Home
Class 12
MATHS
If a, b and c are in H.P., then the valu...

If a, b and c are in H.P., then the value of `((ac+ab-bc)(ab+bc-ac))/(abc)^2` is

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
A, B
`(1/b+1/c-1/a)(1/c+1/a-1b)`
`=(1/b+1/c-2/b+1/c)(1/c+1/b-1/c)`
Also by eliminating b, we get the given expression
`((a+c)(3a-c))/(4a^(2)c^(2))`
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE|Exercise EXERCIESE ( MATRIX MATCH TYPE )|3 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise (Numerical)|28 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise EXERCIESE ( MULTIPLE CORRECT ANSWER TYPE )|1 Videos

  • PROBABILITY II

    CENGAGE|Exercise NUMARICAL VALUE TYPE|2 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise JEE Advanced Previous Year|11 Videos

Similar Questions

Explore conceptually related problems

If a,b, and c are in H.P.then th value of ((ac+ab-bc)(ab+bc-ac))/((abc)^(2)) is ((a+c)(3a-c))/(4a^(2)c^(2)) b.(2)/(bc)-(1)/(b^(2)) c.(2)/(bc)-(1)/(a^(2)) d.((a-c)(3a+c))/(4a^(2)c^(2))

If a,b,c be the sum of n term of three A.P\'s whose first terms are unity and common differences are in H.P., then n= (A) (2ac+ab+bc)/(a+c-ab) (B) (2ac-ab-bc)/(a+c-ab) (C) (2ac-ab-bc)/(a+c-ab) (D) (2ac-ab+bc)/(a+c-ab)

If bc + ab + ca = abc, then the value of (b+c)/(bc(1-a))+(a+c)/(ac(1-b))+(a+b)/(ab(1-c)) is

If a:b=4:5 and b:c=2:3, then a:c=

What is the value of |(-a^(2),ab,ac),(ab,-b^(2),bc),(ac,bc,-c^(2))| ?

If a,b,c are in A.P. prove that: (i) (ab)^(-1),(ca)^(-1) and (bc)^(-1) are also in A.P. (ii) (ab+ac)/(bc),(bc+ca)/(ca),(ca+cb)/(ab) are also in A.P.

If a+b+c = 7 and ab+bc+ac= -6, then the value of a^3+b^3+c^3-3abc is: / यदि a+b+c = 7 तथा ab+bc+ac= -6 है, तो a^3+b^3+c^3-3abc का मान क्या होगा ?

If a^2+b^2+c^2=ab+bc+ac then the value of (a+c)/b is:- यदि a^2+b^2+c^2=ab+bc+ac हो, तो (a+c)/b का मान क्या होगा ?

CENGAGE-PROGRESSION AND SERIES-Exercise (Multiple & Comprehension)
  1. 1/(sqrt(2)+sqrt(5))+1/(sqrt(5)+sqrt(8))+1/(sqrt(8)+sqrt(11))+ n terms ...

    Text Solution

    |

  2. Given that x+y+z =15 when a,x,y,z,b are in A.P and 1/x+1/y+1/z=5/3 whe...

    Text Solution

    |

  3. If a, b and c are in H.P., then the value of ((ac+ab-bc)(ab+bc-ac))/(a...

    Text Solution

    |

  4. If p,q and r are in A.P then which of the following is / are true ?

    Text Solution

    |

  5. If x^2+9y^2+25 z^2=x y z((15)/2+5/y+3/z),t h e n x ,y ,a n dz are in ...

    Text Solution

    |

  6. If A1, A2, G1, G2, ; a n dH1, H2 are two arithmetic, geometric and har...

    Text Solution

    |

  7. If 1/(b-a)+1/(b-c)=1/a+1/c , then a ,b ,a n dc are in H.P. a ,b ,a n d...

    Text Solution

    |

  8. If a,b,c are three distinct numbers in G.P., b,c,a are in A.P and a,bc...

    Text Solution

    |

  9. If a,b,c are in A.P and a^2,b^2,c^2 are in H.P then which is of the fo...

    Text Solution

    |

  10. If first and (2n-1)^(th) terms of A.P., G.P. and H.P. are equal and th...

    Text Solution

    |

  11. Let E=1/(1^2)+1/(2^2)+1/(3^2)+ Then, E<3 b. E >3//2 c. E >2 d. E<2

    Text Solution

    |

  12. Sum of certain consecutive odd positive intergers is 57^2 -13^2 The l...

    Text Solution

    |

  13. Sum of certain consecutive odd positive intergers is 57^2 -13^2 The l...

    Text Solution

    |

  14. Sum of certain consecutive odd positive intergers is 57^2 -13^2 The l...

    Text Solution

    |

  15. Consider three distinct real numbers a,b,c in a G.P with a^2+b^2+c^2=t...

    Text Solution

    |

  16. Consider three distinct real numbers a,b,c in a G.P with a^2+b^2+c^2=t...

    Text Solution

    |

  17. If a, b and c also represent the sides of a triangle and a,b,c are in ...

    Text Solution

    |

  18. In a n increasing G.P. , the sum of the first and the last term is ...

    Text Solution

    |

  19. In a n increasing G.P. , the sum of the first and the last term is ...

    Text Solution

    |

  20. In a G.P the sum of the first and last terms is 66, the product of the...

    Text Solution

    |