Home
Class 11
MATHS
The ratio of the.A.M. and G.M. of two po...

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)))`

Promotional Banner

Topper's Solved these Questions

  • MODEL PAPER (12)

    JBD PUBLICATION|Exercise EXERCISE|40 Videos

  • MODEL PAPER (14)

    JBD PUBLICATION|Exercise EXERCISE|39 Videos

Similar Questions

Explore conceptually related problems

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

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.

The ratio of the sums of m and n terms of an A.P. is m^2: n^2 . Show that the ratio of m^(th) and n^(th) term is (2m - 1 ) : (2n -1).

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)) .

The sum of two numbers is 6 times their G.M. show that numbers are in the ratio 3+2sqrt2: 3-2sqrt2 .

If the ratio of the sum of m terms of an A.P. to the sum of n terms is m2 : n2. Show that the ratio of the 5th to 11th term is 3 : 7.

Two positive numbers whose difference is 12 and whose A.M. exceeds the G.M by 2 are:

If (sin A)/(sin B)=m , and (cosA)/(cosB)=n , prove that tan A= +- m/n sqrt ((1-n^2)/(m^2-1)) .

Evaluate int cosmx cosnx dx , where m,n are positive integers and m ne n . What happens if m=n?

JBD PUBLICATION-MODEL PAPER (13)-EXERCISE
  1. Prove that:(tan^2 20- tan^2 theta)/(1- tan^2 20 tan^2 theta)=tan30 tan...

    Text Solution

    |

  2. Prove, by Mathematical Induction, that for all n in N, 2.7^n+3.5^n-5...

    Text Solution

    |

  3. How many different numbers between 100 and 1000 can be formed from the...

    Text Solution

    |

  4. The ratio of the.A.M. and G.M. of two positive numbers a and b is m : ...

    Text Solution

    |

  5. If the sum to infinity of the series 3+5r+7r^2+………is 44/9. Find r.

    Text Solution

    |

  6. The line 2x-3y=4 is perpendicular bisector of the line AB. If the coor...

    Text Solution

    |

  7. Find the equation of ellipse whose vertices are (pm13,0) and foci are ...

    Text Solution

    |

  8. Find underset(xrarr1)lim f(x), where f(x)={(x^2-1, x le 1),(-x^2-1, x>...

    Text Solution

    |

  9. Find the derivative of x^4-5 at x=10.

    Text Solution

    |

  10. In a single throw of two dice, find the probability of total of 9 or I...

    Text Solution

    |

  11. A bag contains 5 black and 3 white balls. Two balls are drawn at rando...

    Text Solution

    |

  12. A bag contains 5 black and 3 white balls. Two balls are drawn at rando...

    Text Solution

    |

  13. Convert z= (i-1)/(cos frac (pi)(3)+i sin frac (pi)(3)) in polar form.

    Text Solution

    |

  14. Find the modulus and argument of the complex number (1+2 i)/(1- 3i)

    Text Solution

    |

  15. Solve the following system of inequalities graphically: x + 2y le ...

    Text Solution

    |

  16. In an experiment, a solution of a hydrochloric acid is to be kept betw...

    Text Solution

    |

  17. Evaluate: underset(xrarrpi/4)lim (cosx-sinx)/(x-pi/4).

    Text Solution

    |

  18. Find the derivative of sin(x+1) w.r.t. x

    Text Solution

    |

  19. Find the variance and S.D of the following set of numbers: 25,50,45,30...

    Text Solution

    |

  20. Find the mean deviation about the mean of the following data:

    Text Solution

    |