Home
Class 12
MATHS
If a, b, c are in geometric progression,...

If a, b, c are in geometric progression, then show that,
`(a^(2) + ab + b^(2))/(ab + bc + ca) = (a + b)/(b + c)`

Promotional Banner

Topper's Solved these Questions

  • SEQUENCE AND SERIES

    CHHAYA PUBLICATION|Exercise Exercise 9 C (Long Answer Type Questions)|35 Videos

  • SEQUENCE AND SERIES

    CHHAYA PUBLICATION|Exercise Exercise 9 D (Multiple Choice Type Questions)|2 Videos

  • SEQUENCE AND SERIES

    CHHAYA PUBLICATION|Exercise Exercise 9 C (Very Short Answer Type Questions)|17 Videos

  • SECOND ORDER DERIVATIVE

    CHHAYA PUBLICATION|Exercise Sample Question for Competitive Examination (Assertion-Reason type)|2 Videos

  • SET THEORY

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos

Similar Questions

Explore conceptually related problems

If a, b, c are In A.P., then show that, a^(2)(b+c), b^(2)(c+a), c^(2)(a+b) are in A.P. (ab+bc+ca != 0)

If a, b, c are in G.P., show that a^(2) + b^(2), ab + bc and b^(2) + c^(2) are also in G.P.

Prove (a + b + c) (ab + bc + ca) > 9abc

If a, b and c are three positive real numbers, show that a^2 + b^2 + c^2 ge ab + bc + ca

Three numbers a,b,c are such that (a^(2) +ab+b ^(2))/(ab +bc +ca) =(a+b)/(a+c), then the numbers b, a, c are in-

If a, b, c are positive, prove that (a + b + c) (ab + bc + ca) ge 9abc.

If a, b, c are in A.P., show that, (bc)/(a(b+c)), (ca)/(b(c+a)) and (ab)/(c(a+b)) are in H.P.

Find the product (2a + b+c) (4a ^(2) + b ^(2) + c ^(2) - 2ab -bc -2ca)

If a, b, c are all positive, prove that 6abc le bc(b + c) + ca(c + a) + ab(a + b)

CHHAYA PUBLICATION-SEQUENCE AND SERIES-Exercise 9 C (Short Answer Type Questions)
  1. If a, b, c and d are in G.P., show that, (b-c)^(2) + (c-a)^(2)+ (d-b...

    Text Solution

    |

  2. If three numbers a, b, c satisfy the relation (a^(2) + b^(2)) (b^(2) +...

    Text Solution

    |

  3. If a, b, c are in geometric progression, then show that, (a^(2) + ab...

    Text Solution

    |

  4. A boy saves 1 paisa the first day, 2 paise the second day, 4 paise the...

    Text Solution

    |

  5. Shri A. K. Roy borrows Rs. 6000 to repay the amount with interest of R...

    Text Solution

    |

  6. A man borrows Rs. 19682 without interest and agrees to repay the money...

    Text Solution

    |

  7. The A.M. of two numbers is 15 and their G.M. is 12. Find the numbers.

    Text Solution

    |

  8. If a, b, c are in G.P. and x, y be the A.M. between a, b and b, c resp...

    Text Solution

    |

  9. If a, b, c are in G.P. and x, y be the A.M. between a, b and b, c resp...

    Text Solution

    |

  10. If a, b, c be in A.P. and x, y, z be in G.P., prove that, x^(b-c).y^...

    Text Solution

    |

  11. The sum of three numbers in G.P. is 70. If each of the two extremes be...

    Text Solution

    |

  12. Let t(r) be the rth term of an A.P. If t(2), t(8) and t(32) are in G.P...

    Text Solution

    |

  13. If p, q, r be in arithmetic progression, then show that the pth, qth a...

    Text Solution

    |

  14. The nth term of a series is 3^(n) + 2n, find the sum of first n terms ...

    Text Solution

    |

  15. If one arithmetic mean A and two geometric means p, q be inserted betw...

    Text Solution

    |

  16. If A is the A.M. and G is the G.M. of two unequal positive real number...

    Text Solution

    |

  17. Between two positive real numbers a and b, one arithmetic mean A and t...

    Text Solution

    |

  18. If a, b, c are in G.P. and the equation ax^(2) + 2bx + c = 0 and dx^(2...

    Text Solution

    |

  19. If a is A.M. of two positive numbers b and c and two G.M's between b a...

    Text Solution

    |

  20. If G is the G.M. between two positive numbers a and b, show that (1)/(...

    Text Solution

    |