Home
Class 12
MATHS
If 1/(b-a)+1/(b-c)=1/a+1/c , then a ,b ,...

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 dc` are in A.P. `b=a+c` `3a=b+c`

A

a,b, and c are in H.P

B

a,b, and c are in A.P

C

b=a+c

D

3a= b+c

Text Solution

Verified by Experts

The correct Answer is:
A, B
`1/(b-a)+1/(b-c)=1/a+1/c`
or `1/(b-a)-1/c=1/a-1/(b-c)`
or `(c-b+a)/(c(b-a))=(b-c-a)/(a(b-c))`
`rArrc-b+a=0` or `1/(c(b-a))=1/(a(c-b))`
`rArrb=a+c` or bc-ac=ac-ab
`rArrb=a+c`or `b=(2ac)/(a+c)`
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 1/(b-a)+1/(b-c)=1/a+1/c , then A. a ,b ,a n dc are in H.P. B. a ,b ,a n dc are in A.P. C. b=a+c D. 3a=b+c

If l n(a+c),l n(a-c)a n dl n(a-2b+c) are in A.P., then (a) a ,b ,c are in A.P. (b) a^2,b^2, c^2, are in A.P. (c) a ,b ,c are in G.P. d. (d) a ,b ,c are in H.P.

If (1)/(a)+(1)/(a-b)+(1)/(c)+(1)/(c-b)=0 and a+c-b!=0, then prove that a,b,c are in H.P.

If a,b,c, are in A.P., b,c,d are in G.P. and c,d,e, are in H.P., then a,c,e are in

If a,b,c are in H.P , b,c,d are in G.P and c,d,e are in A.P. , then the value of e is

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

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

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

CENGAGE-PROGRESSION AND SERIES-Exercise (Multiple & Comprehension)
  1. 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

    |

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

    Text Solution

    |

  3. 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

    |

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

    Text Solution

    |

  5. 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

    |

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

    Text Solution

    |

  7. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. Four different integers form an increasing A.P .One of these numbers i...

    Text Solution

    |

  18. The sum of all the four numbers is

    Text Solution

    |

  19. The common difference of the divisible by

    Text Solution

    |

  20. Consider the sequence in the form of group (1),(2,2)(3,3,3),(4,4,4,4),...

    Text Solution

    |