Home
Class 11
MATHS
If a be the A.M. and x, y be the two G.M...

If a be the A.M. and x, y be the two G.M's between b and c, show that
`x^3+y^3=2abc`.

Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    JBD PUBLICATION|Exercise EXAMPLE|54 Videos

  • RELATIONS AND FUNCTIONS

    JBD PUBLICATION|Exercise EXAMPLE|35 Videos

  • SETS

    JBD PUBLICATION|Exercise EXAMPLE|58 Videos

Similar Questions

Explore conceptually related problems

Insert 3 A.M.’s between 3 and 19.

If a,b,c are in AP and p is the AM between a and b and q is the AM between b and c, then show that b is the AM between p and q.

a, b, c are in G.P. and x and y are the A.M.’s between a, b and b, c respectively. Show that : a/x+c/y=2 .

a, b, c are in G.P. and x and y are the A.M.’s between a, b and b, c respectively. Show that : 1/x+1/y=2/b .

If A_1 and A_2 are two A.M.’s between a and b, prove that : A_1+A_2 =a+b .

Find the A.M. between : 3.7 and 5.5.

The ratio of the A.M. and G.M. of two positive numbers a and b, is m : n. Show that a:b=(m+ sqrt(m^2-n^2)): (m-sqrt(m^2-n^2)) .

If a,b,c are in A.P. and x,y,z are in G.P., then show that x^(b-c).y(c-a).z(a-b)=1 .

If A is the A.M. between a and b, prove that : 4(a-A)(A-b)=(a-b)^(2) .

If a is the A.M. of b and c and the two geometric means are G_(1) and G_(2) , then prove that G_(1)^(3)+G_(2)^(3) = 2abc

JBD PUBLICATION-SEQUENCES AND SERIES-EXAMPLE
  1. Find the sum of n terms of the following sequences: 8+88+888+……………..up...

    Text Solution

    |

  2. The A.M. between two positive numbers is 34 and their G.M. is 16. find...

    Text Solution

    |

  3. If a be the A.M. and x, y be the two G.M's between b and c, show that ...

    Text Solution

    |

  4. The sum of three numbers which are consecutive terms of an A.P. is 21....

    Text Solution

    |

  5. If a,b,c are in A.P. and x,y,z are in G.P., then show that x^(b-c).y(c...

    Text Solution

    |

  6. Find a G.P. for which sum of the first two terms is -4 and the fifth t...

    Text Solution

    |

  7. The sum of an inifinite G.P. is 8. If the second term is 2, then find ...

    Text Solution

    |

  8. Find the sum to n terms of the series 3 xx 8 + 6 xx 11 + 9 xx 14 + …

    Text Solution

    |

  9. Find the sum of the series 1*n+2*(n-1)+3*(n-2)+4*(n-3)+"..."+(n-1)*2+n...

    Text Solution

    |

  10. The difference between any two consecutive interior angles of a polygo...

    Text Solution

    |

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

    Text Solution

    |

  12. If A.M and G.M of two positive numbers are 13 and 12 respectively. Fin...

    Text Solution

    |

  13. Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

    Text Solution

    |

  14. The ratio of the sums of m and n terms of an A.P. is m^2: n^2. Show th...

    Text Solution

    |

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

    Text Solution

    |

  16. If S(1),S(2),S(3)be respectively the sum of n, 2n and 3n terms of a GP...

    Text Solution

    |

  17. Let S be the sum, P the product and R the sum of reciprocals of n term...

    Text Solution

    |

  18. Let S be the sum, P the product and R the sum of reciprocals of n term...

    Text Solution

    |

  19. The sum of two numbers is 6 times their geometric mean, show that numb...

    Text Solution

    |

  20. The sum of two numbers is 6 times their geometric mean, show that numb...

    Text Solution

    |