Home
Class 11
MATHS
If (a-b), (b-c), (c-a) are in GP then pr...

If (a-b), (b-c), (c-a) are in GP then prove that `(a+b+c)^2 =3(ab+bc+ca)..`

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|9 Videos
  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

If a, b, c are in GP then prove that a^3, b^3, c^3 are in GP.

If a, b, c are in GP then prove that, (a+2b+2c)(a-2b+2c)= a^2+ 4c^2

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

If a,b, c are in GP, Prove that a^2, b^2 , c^2 are in GP.

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

If a,b,c are in GP, Prove that, a(b^2+c^2) =c(a^2+b^2)

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

If a : b = b : c , then prove that (abc(a+b+c)^(3))/((ab+bc+ca)^(3)) = 1

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.

CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. Express the given complex number in (a+ib) form: (5-2i)^2

    Text Solution

    |

  2. If S denotes the sum to infinity and Sn the sum of n terms of the seri...

    Text Solution

    |

  3. If (a-b), (b-c), (c-a) are in GP then prove that (a+b+c)^2 =3(ab+bc+ca...

    Text Solution

    |

  4. Given that x+y+z=15 when a ,x ,y ,z ,b are in A.P. and 1/x+1/y+1/z=5/3...

    Text Solution

    |

  5. Let a1,a2,a3…… ,an be in G.P such that 3a1+7a2 +3a3-4a5=0 Then find c...

    Text Solution

    |

  6. The 9th term of the series 27+9+52/5+36/7+.... will be (a) 110/17 (b...

    Text Solution

    |

  7. If a, b, c are in GP then prove that, (a+2b+2c)(a-2b+2c)= a^2+ 4c^2

    Text Solution

    |

  8. If sum(r=1)^n r(r+1)(2r+3)=a n^4+b n^3+c n^2+d n+e , then (a) a-b=d-c ...

    Text Solution

    |

  9. If a,b,c,d are in GP then prove thst (b+c)(b+d) =(c+a)(c+d)

    Text Solution

    |

  10. If a,x,b are in A.P.,a,y,b are in G.P. and a,z,b are in H.P. such that...

    Text Solution

    |

  11. If a,b, and c are in G.P then a+b,2b and b+ c are in

    Text Solution

    |

  12. If in a progression a1, a2, a3,.......... e tc dot,(ar-a(r+1)) bears...

    Text Solution

    |

  13. a ,b ,c x in R^+ such that a ,b ,and c are in A.P. and b ,c and d ar...

    Text Solution

    |

  14. Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic equ...

    Text Solution

    |

  15. Let a in (0,1] satisfies the equation a^(2008)-2a+1=0 and S=1+a+a^2+.....

    Text Solution

    |

  16. If a ,b and c are in A.P. and b-a ,c-b and a are in G.P., then a : b :...

    Text Solution

    |

  17. If a ,b ,a n dc are in A.P. p ,q ,a n dr are in H.P., and a p ,b q ,a ...

    Text Solution

    |

  18. The sum of three numbers in G.P. is 14. If one is added to the first ...

    Text Solution

    |

  19. If x ,2x+2 and 3x+3 are the first three terms of a G.P., then the four...

    Text Solution

    |

  20. The harmonic mean of two numbers is 4. Their arithmetic mean A and the...

    Text Solution

    |