Home
Class 11
MATHS
If A and G be A.M. and G.M., respectivel...

If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are `A +- sqrt((A+G)(A-G))`.

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

If A and G are the A.M. and G.M. respectively between any two distinct positive numbers a and b then show that A > G.

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

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

If one G.M., G and two A.M's p and q be inserted between two given numbers, prove that G^(2)= (2p-q) (2q-p)

If the ratio of A.M and G.M between two numbers is 5:3, then the ratio of two numbers is:

A.M. between two numbers is 10 and their G.M is 8. Find the numbers.

Find two positive numbers m and n whose AM and GM are 34 and 16 respectively.

If the A.M of two numbers is 9 and G.M is 4, then these numbers are roots of the equation:

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 G is the geometric mean between two distinct positive numbers a and b, then show that 1/(G-a)+1/(G-b)=1/G .

PSEB-SEQUENCES AND SERIES-EXERCISE
  1. Find the value of n so that (a^(n+1)+ b^(n+1))/(a^n+b^n) may be the ge...

    Text Solution

    |

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

    Text Solution

    |

  3. If A and G be A.M. and G.M., respectively between two positive numbers...

    Text Solution

    |

  4. The number of bacteria in a certain culture doubles every hour. If the...

    Text Solution

    |

  5. What will Rs 500 amounts to in 10 years after its deposit in a bank wh...

    Text Solution

    |

  6. If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respect...

    Text Solution

    |

  7. Find the sum to n terms of the series given below:- 1xx2 + 2xx3 + 3xx4...

    Text Solution

    |

  8. Find the sum to n terms of the series given below:- 1xx2xx3 + 2xx3xx4 ...

    Text Solution

    |

  9. Find the sum to n terms of the series given below:- 3xx1^2+5xx2^2+7xx3...

    Text Solution

    |

  10. Find the sum to n terms of the series given below:- 1/(1xx2)+1/(2xx3)+...

    Text Solution

    |

  11. Find the sum to n terms of the series given below:- 5^2 + 6^2 + 7^2 + ...

    Text Solution

    |

  12. Find the sum to n terms of the series given below whose nth terms is g...

    Text Solution

    |

  13. Find the sum to n terms of the series given below whose nth terms is g...

    Text Solution

    |

  14. Find the sum to n terms of the series given below whose nth terms is g...

    Text Solution

    |

  15. Show that the sum of (m+n)^(th) and (m -n)^(th) terms of an A.P. is eq...

    Text Solution

    |

  16. If the sum of three numbers in A.P., is 24 and their product is 440, f...

    Text Solution

    |

  17. Let the sum of n, 2n, 3n terms of an A.P. be S1, S2 and S3, respective...

    Text Solution

    |

  18. Find the sum of all numbers between 200 and 400 which are divisible by...

    Text Solution

    |

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

    Text Solution

    |

  20. Find the sum of all two digit numbers which when divided by 4, yields ...

    Text Solution

    |