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

If `a^2,b^2,c^2` are in A.P., then prove that the following are also in A.P. (i)`1/(b+c),1/(c+a),1/(a+b)` (ii) `a/(b+c),b/(c+a),c/(a+b)`

Text Solution

Verified by Experts

`2b2 = a2 + c2 [as a2 b2 c2` are in A.P.]
`=> b2 + b2 = a2 + c2`
`=> b2 - a2 = c2 - b2`
`=> (b-a) (b+a) = (c-b) (c+b)`
...
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    RD SHARMA|Exercise Solved Examples And Exercises|228 Videos

Similar Questions

Explore conceptually related problems

If a, b, c are in A.P. that the following are also in A.P:(i) (1)/(bc),(1)/(ca),(1)/(ab)

If a^(2),b^(2),c^(2) are in A.P.then prove that cot A,cot B,cot C are in A.P.

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

If a,b,c are in AP , then prove that : b+c,c+a,a+b are also in AP

If a,b,c are in A.P.then prove that the following are also in A.P.(1)/(sqrt(b)+sqrt(c)),(1)/(sqrt(c)+sqrt(a)),(1)/(sqrt(a)+sqrt(b))

If a^(2),b^(2),c^(2) are in A.P.prove that cot A,cot B,cot C are in A.P.

If a,b,c are in A.P.prove that b+c,c+a,a+b are also in A.P.

RD SHARMA-ARITHMETIC PROGRESSIONS-Solved Examples And Exercises
  1. If (b-c)^2,(c-a)^2,(a-b)^2 are in A.P., then prove that 1/(b-c),1/(c-a...

    Text Solution

    |

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

    Text Solution

    |

  3. If a^2,b^2,c^2 are in A.P., then prove that the following are also in...

    Text Solution

    |

  4. Two cars start together in the same direction from the same place. The...

    Text Solution

    |

  5. Find an A.P. in which the sum of any number of terms is always three ...

    Text Solution

    |

  6. If log2,log(2^x-1),log(2^x+3) are in A.P., write the value of xdot

    Text Solution

    |

  7. The sums of first n terms of two A.P. ' s are in hte ratio (7n+2):(n+4...

    Text Solution

    |

  8. Give first 3 terms of the sequence defined by an=n/(n^2+1)dot

    Text Solution

    |

  9. First term of a sequence is 1 and (n+1)th term is obtained by adding (...

    Text Solution

    |

  10. 1,4,7,10,is an A.P. whose first term is 1 and the common difference is...

    Text Solution

    |

  11. 11, 7, 3, -1 is an A.P. whose first term is 11 and the common diffe...

    Text Solution

    |

  12. The nth term of a sequence is 3n-2 is the sequence an A.P.? If so, fin...

    Text Solution

    |

  13. If the nth term an\ of a sequence is given by an=n^2-n+1 write down i...

    Text Solution

    |

  14. A sequence is defined by an=n^3-6n^2+11 n-6. Show that the first three...

    Text Solution

    |

  15. Find the first four terms of the sequence defined by a1=3\ a n d\ an=3...

    Text Solution

    |

  16. Write the first five terms in each of the following sequence: a1=1,\ a...

    Text Solution

    |

  17. Write the first five terms in each of the following sequence: a1=1=\ a...

    Text Solution

    |

  18. Write the first five terms in each of the following sequence: a1=a2=2,...

    Text Solution

    |

  19. The Fibonacci sequence is defined by a1=1=a2,\ an=a(n-1)+a(n-2) for n ...

    Text Solution

    |

  20. Show that each of the following sequences is an A.P. Also, find the ...

    Text Solution

    |