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

  • SEQUENCES AND SERIES

    NCERT BANGLISH|Exercise EXERCISE 9.4|10 Videos
  • RELATIONS AND FUNCTIONS

    NCERT BANGLISH|Exercise Miscellaneous Exercise on Chapter 2|12 Videos
  • SETS

    NCERT BANGLISH|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 1|26 Videos

Similar Questions

Explore conceptually related problems

If A and G are the A.M.and G.M. of two unequal positive numbers a and b, show that A>G>G^2/A

If the ratio of A.M. of two numbers x and y to their G.M. is p : q, show that, x : y = (p + sqrt(p^(2) - q^(2))) : (p- sqrt(p^(2) - q^(2)))

If the A.M. of two positive numbers aa n db(a > b) is twice their geometric mean. Prove that : a : b=(2+sqrt(3)):(2-sqrt(3))dot

If A.M. and G.M. of two positive numbers a and b are 10 and 8, respectively, find the numbers.

If A and G be the A.M. and G.M. of two numbers , show that the numbers are A +- sqrt(A^(2) - G^(2)) .

If A.M. and G.M. between two numbers is in the ratio m : n then prove that the numbers are in the ratio (m+sqrt(m^2-n^2)):(m-sqrt(m^2-n^2))dot

If A.M. and G.M. of two positive real numbers are 25 and 15 respectively, then find their H.M.

If A is the A.M. and G is the G.M. of two unequal positive real numbers p and q, prove that A gt G and |G| gt (G^(2))/(A)

If A.M and G.M of two positive real numbers are 25 and 15 respectively, then find their H.M.

If the A.M. and G.M. of two positive real nos. are 45 and 9 respectively, then find their H.M.

NCERT BANGLISH-SEQUENCES AND SERIES-Miscellaneous Exercise On Chapter 9
  1. If (a+bx)/(a-bx)=(b+cx)/(b-cx)=(c+dx)/(c-dx)( x ne 0) then show that ...

    Text Solution

    |

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

    Text Solution

    |

  3. The p^(th), q^(th) and r^(th) terms of an A.P. are a, b, c, respectiv...

    Text Solution

    |

  4. If a(1/b+1/c),b(1/c+1/a),c(1/a+1/b) are in A.P., prove that a,b,c are...

    Text Solution

    |

  5. If a, b, c, d are in G.P, prove that (a^n + b^n), (b^n + c^n), (c^n +...

    Text Solution

    |

  6. If a and b are the roots of x^2 – 3x + p = 0 and c, d are roots of x^...

    Text Solution

    |

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

    Text Solution

    |

  8. If a, b, c are in A.P., b, c, d are in G.P. and 1/c,1/d,1/e are in A.P...

    Text Solution

    |

  9. Find the sum of the following series up to n terms: 5+55+555+......

    Text Solution

    |

  10. Find the 20^(th) term of the series 2 xx 4 + 4 xx 6 + 6 xx 8 + ... + ...

    Text Solution

    |

  11. Find the sum of the first n terms of the series: 3+ 7 +13 +21 +31 +......

    Text Solution

    |

  12. If S1, S2, S3 are the sum of first n natural numbers, their squares a...

    Text Solution

    |

  13. Find the sum of the following series up to n terms: 1^3/1+(1^3+2^3)/...

    Text Solution

    |

  14. Show that (1xx2^2+2xx3^2+...+nxx(nxx1)^2)/(1^2xx2+2^2xx3+...+n^2xx(n+1...

    Text Solution

    |

  15. A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and ag...

    Text Solution

    |

  16. Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agr...

    Text Solution

    |

  17. A person writes a letter to four of his friends. He asks each one of t...

    Text Solution

    |

  18. A man deposited Rs 10000 in a bank at the rate of 5% simple interest a...

    Text Solution

    |

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

    Text Solution

    |

  20. 150 workers were engaged to finish a job in a certain number of days. ...

    Text Solution

    |