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)`

Text Solution

Verified by Experts

Given, `(a-b),\ (b-c),(c-a)`

are in G.P

`(b-c)^2=(a-b)(c-a)`

`b^2+c^2-2bc=ac-bc-a^2+ab`

`a^2+b^2+c^2=ac+bc+ab`

We know,

`(a+b+c)^2=a^2+b^2+c^2+2(a b+b c+c a)`

`(a+b+c)^2=ac+bc+ab+2(a b+b c+c a)`

...
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    RD SHARMA|Exercise Solved Examples And Exercises|157 Videos

  • GRAPHS OF TRIGONOMETRIC FUNCTIONS

    RD SHARMA|Exercise Solved Examples And Exercises|5 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 (b+c),(c+a),(a+b) are in H. P.then prove that (a)/(b+c),(b)/(c+a),(c)/(a+b) 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.

If a,b,c are in G.P.and b-c,c-a,a-b are in H.P.then prove that a+b+c=-3(ac)^((1)/(2))

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

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

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.then prove that (a^(2)+ab+b^(2))/(bc+ca+ab)=(b+a)/(c+b)

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

If a, b, c are in GP, prove that a^(2), b^(2), c^(2) are in GP.

RD SHARMA-GEOMETRIC PROGRESSIONS-Solved Examples And Exercises
  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 respectivel...

    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., then 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. If ax^2+2bx+c=0and x^2...

    Text Solution

    |

  13. If a, b,c and d are distinct positive no in AP. then

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. Insert 5 geometric means between (32)/9 and (81)/2

    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 and a ...

    Text Solution

    |

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

    Text Solution

    |

  20. If a is the G.M. of 2 and 1/4, find a

    Text Solution

    |