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If the arithmetic means of two positive number a and b `(a gt b )` is twice their geometric mean, then find the ratio a: b

A

`2+sqrt(3 ):2-sqrt(3)`

B

`7 +4 sqrt(3) :1`

C

`1 : 7-4sqrt(3)`

D

`2 : sqrt(3)`

Text Solution

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The correct Answer is:
1,2,3
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Knowledge Check

  • If the A.M of two positive numbers a and b, (a gt b) is twice their G.M. , then a:b is :

    A
    a)`2: sqrt3`
    B
    b)`2:7 + 4sqrt3`
    C
    c)`2+ sqrt3 : 2-sqrt3`
    D
    d)`7+4sqrt3 :7-4sqrt3`

  • If the arithmetic mean between a and b equals n times their geometric mean, then find the ratio a : b.

    A
    `(2n^2 + 1) pm 2n sqrt(n^2 -1)`
    B
    `(2n^2 - 1) pm 2n sqrt(n^2 - 1)`
    C
    `(2n^2 - 1) pm 2n sqrt(n^2 + 1)`
    D
    none of these

  • The arithmetic mean of two positive numbers a and b exceeds their geometric mean by 2 and the harmonic mean is one - fifth of the greater of a and b, such that alpha=a+b and beta=|a-b| , then the value of alpha+beta^(2) is equal to

    A
    96
    B
    234
    C
    74
    D
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