Home
Class 11
MATHS
If (a-b),\ (b-c),(c-a) are in G.P. then ...

If `(a-b),\ (b-c),(c-a)` are in G.P. then prove that `(a+b+c)^2=3(a b+b c+c a)`

Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    RD SHARMA ENGLISH|Exercise All Questions|200 Videos

  • GRAPHS OF TRIGONOMETRIC FUNCTIONS

    RD SHARMA ENGLISH|Exercise All Questions|22 Videos

Similar Questions

Explore conceptually related problems

If a,b,c are in G.P., then show that a(b-c)^2=c(a-b)^2

If a ,b ,c are in G.P. then prove that (a^2+a b+b^2)/(b c+c a+a b)=(b+a)/(c+b)

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

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

If a ,b ,c ,d are in G.P. prove that: (a b-c d)/(b^2-c^2)=(a+c)/b

If (b-c)^2,(c-a)^2,(a-b)^2 are in A.P., then prove that 1/(b-c),1/(c-a),1/(a-b) are also in A.P.

If (b-c)^2,(c-a)^2,(a-b)^2 are in A.P., then prove that 1/(b-c),1/(c-a),1/(a-b) are also in A.P.

If (b-c)^2,(c-a)^2,(a-b)^2 are in A.P., then prove that 1/(b-c),1/(c-a),1/(a-b) are also in A.P.

If a ,b ,c are in G.P., prove that: a(b^2+c^2)=c(a^2+b^2)

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

RD SHARMA ENGLISH-GEOMETRIC PROGRESSIONS-All Questions
  1. If a ,\ b\ c are in G.P., prove that the following are also in G.P.: a...

    Text Solution

    |

  2. If a, b, c are in G. P., prove that a^2+ b^2, ab + bc, b^2 +c^2 are al...

    Text Solution

    |

  3. If (a-b),\ (b-c),(c-a) are in G.P. then prove that (a+b+c)^2=3(a b+b c...

    Text Solution

    |

  4. If the 4th, 10th and 16th terms of a G.P. are x, y, and z  respect...

    Text Solution

    |

  5. If a, b, c are in A.P and a, b, d are in G.P, prove that a, a -b, d ...

    Text Solution

    |

  6. If the pth, qth, rth, and sth terms of an A.P. are in G.P., t hen p-q ...

    Text Solution

    |

  7. If a ,\ b ,\ c are in A.P. b ,\ c ,\ d are in G.P. and 1/c ,1/d ,1/e a...

    Text Solution

    |

  8. If a, b, c are in A.P and a, b, d are in G.P, prove that a, a -b, d ...

    Text Solution

    |

  9. If p^(t h),\ q^(t h),\ a n d\ r^(t h) terms of an A.P. and G.P. are bo...

    Text Solution

    |

  10. Find two numbers whose arithmetic mean is 34 and the geometric mean is...

    Text Solution

    |

  11. If A.M. and G.M. between two numbers is in the ratio m : n then prove...

    Text Solution

    |

  12. a,b,c are positive real numbers forming a G.P. ILf ax^2+2bx+c=0and ...

    Text Solution

    |

  13. Q. If a, b,c and d are distinct positive no. in AP. then (A) ad lt ...

    Text Solution

    |

  14. Insert 6 geometric means between 27 and 1/(81)dot

    Text Solution

    |

  15. Insert 5 geometric means between 16 and 1/4dot

    Text Solution

    |

  16. Insert 5 geometric means between (32)/9a n d(81)/2dot

    Text Solution

    |

  17. Find the geometric means of the following pairs of number: 2 and 8.

    Text Solution

    |

  18. Find the geometric means of the following pairs of number: a^3b\ a n d...

    Text Solution

    |

  19. Find the geometric means of the following pairs of number: -8\ a n d-2...

    Text Solution

    |

  20. If a is the G.M. of 2\ a n d1/4, find adot

    Text Solution

    |