Home
Class 11
MATHS
If b^2+c^2, c^2+a^2, a^2+b^2 are in A.P....

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

Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise EXERCISE|435 Videos

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise EXERCISE|226 Videos

  • SETS

    MODERN PUBLICATION|Exercise EXERCISE|381 Videos

Similar Questions

Explore conceptually related problems

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

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

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

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

If a, b, c are in A.P., prove that : (bc)^-1,(ca)^-1 and (ab)^-1 are also in A.P.

If a, b, c are in A.P., prove that : (ab+ac)/(bc), (bc+ba)/ (ca), (ca+cb)/(ab) are also in A.P.

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

If a, b, c are in A.P., prove that : (a(b+c))/(bc), (b(c+a))/ (ca), (c(a+b))/(ab) are also in A.P.

If a,b,c are in A.P. then :

If a+b+c ne 0 and (b + c)/a, (c + a)/b, (a + b)/c are in A.P., prove that : 1/a,1/b,1/c are also in A.P.

MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
  1. Two cars start together in the same direction at the same place.The fi...

    Text Solution

    |

  2. The ages of the students of a class form an A.P. whose common differen...

    Text Solution

    |

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

    Text Solution

    |

  4. If a^(-1),b^(-1),c^(-1),d^(-1) are in A.P., then show that : b=(2ac)/(...

    Text Solution

    |

  5. If a(1)=1, a(2)=5 find the common difference and 5th term of A.P

    Text Solution

    |

  6. If the A.M. between pth and qth terms of an A.P. be equal to the A.M. ...

    Text Solution

    |

  7. If a, b, c are in A.P., prove that : a^3+4b^3+c^3=3b (a^2+c^2).

    Text Solution

    |

  8. If a^2 (b+c),b^2(c+a) , c^2(a+b) are in A.P., show that : either a, b,...

    Text Solution

    |

  9. If the mth, nth and pth terms of a G.P. form three consecutive terms o...

    Text Solution

    |

  10. If x,y,z are in G.P. and a^x= b^y=c^z, prove that logb a. logb c=1.

    Text Solution

    |

  11. We are given two G.P.'s, one with the first term 'a' and common ratio ...

    Text Solution

    |

  12. If Sn represents the sum of n terms of a G.P. whose first term and com...

    Text Solution

    |

  13. If a,b,c are in GP, show that the equations ax^(2)+2bx+c=0 and dx^(2)+...

    Text Solution

    |

  14. Find the derivative of the following y=x+1/x+sinx

    Text Solution

    |

  15. The sum of the first three consecutive terms of G.P. is 13 and the sum...

    Text Solution

    |

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

    Text Solution

    |

  17. 150 workers were engaged to finish a job in a certain number of days. ...

    Text Solution

    |

  18. The height of a plant at a certain date is 1.6 metre. If it increases ...

    Text Solution

    |

  19. If |x|<1 and |y|<1, find the sum to infinity of the series : (x+y)+(x^...

    Text Solution

    |

  20. A manufacturer reckons that the value of a machine, which costs him Rs...

    Text Solution

    |