Home
Class 11
MATHS
If a is the A.M. of b and c and the two...

If `a` is the A.M. of `b` and ` c` and the two geometric means are `G_1` and `G_2` , then prove that `G1^3+G2^3=2a b c`

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 is the A.M. of b and c and the two geometric mean are G_1 and G_2, then prove that G_1^3+G_2^3=2a b cdot

If a be one A.M and G_1 and G_2 be then geometric means between b and c then G_1^3+G_2^3=

If a is the arithmetic mean of b and c, and two geometric means G_(1) and G_(2) are inserted between b and c such that G_(1)^(3)+G_(2)^(3)=lamda abc, then find the value of lamda .

If G is the geometric mean of xa n dy then prove that 1/(G^2-x^2)+1/(G^2-y^2)=1/(G^2)

If G is the geometric mean of xa n dy then prove that 1/(G^2-x^2)+1/(G^2-y^2)=1/(G^2)

If one A.M., A and two geometric means G_1a n dG_2 inserted between any two positive numbers, show that (G1 ^2)/(G2)+(G2 ^2)/(G_1)=2Adot

If a is the A.M. between b and c, b the G.M. between a and c, then show that 1/a,1/c,1/b are in A.P.

If a , b ,c are three distinct positive real numbers in G.P., then prove that c^2+2a b >3ac

G is the geometric mean and p and q are two arithmetic means between two numbers a and b, prove that : G^(2)=(2p-q)(2q-p)

If A and G are the arithmetic and geometric means respectively of two numbers then prove that the numbers are (A+sqrt(A^(2)-G^(2)))and(A-sqrt(A^(2)-G^(2)))

RD SHARMA ENGLISH-GEOMETRIC PROGRESSIONS-All Questions
  1. Find two positive numbers whose difference is 12 an whose A.M. exce...

    Text Solution

    |

  2. If one geometric mean G and two arithmetic means A1a n dA2 be inserted...

    Text Solution

    |

  3. If a is the A.M. of b and c and the two geometric means are G1 and G2...

    Text Solution

    |

  4. If x in R , find the minimum value of the expression 3^x+3^(1-x)dot

    Text Solution

    |

  5. If x ,y ,z are distinct positive numbers, then prove that (x+y)(y+z)(z...

    Text Solution

    |

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

    Text Solution

    |

  7. If 1/(a+b),1/(2b),1/(b+c) are three consecutive terms of an A.P., prov...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  10. The sum of three numbers a ,b ,c in A.P. is 18 . If aa n db are eac...

    Text Solution

    |

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

    Text Solution

    |

  12. If mth, nth and pth terms of a G.P. form three consecutive terms of a ...

    Text Solution

    |

  13. If a ,b ,c are in G.P. and x ,y are the arithmetic means of a ,ba n db...

    Text Solution

    |

  14. If x^a=x^(b//2)z^(b//2)=z^c , then prove that 1/a ,1/b ,1/c are in A.P...

    Text Solution

    |

  15. If a ,b ,c are three distinct real numbers in G.P. and a+b+c=x b , t...

    Text Solution

    |

  16. If the sum of three numbers in G.P. is 38 and their product is 1728, ...

    Text Solution

    |

  17. If the p^(t h) and q^(t h) terms of a G.P. are q and p respectively, s...

    Text Solution

    |

  18. In a finite G.P. the product of the terms equidistant from the begi...

    Text Solution

    |

  19. The product of first three terms of a G.P. is 1000. If 6 added to its ...

    Text Solution

    |

  20. Find three numbers in G.P. whose sum is 52 and the sum of whose pro...

    Text Solution

    |