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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))`.

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The ratio of the A.M.and G.M.of two positive numbers a and b,is : n .Show that a :b=(m+sqrt(m^(2)-n^(2))):(m-sqrt(m^(2)-n^(2)))

If the ratio of A.M. and G.M. of two positive numbers a and b is m : n, then prove that : a:b=(m+sqrt(m^(2)-n^(2))):(m-sqrt(m^(2)-n^(2)))

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 A.M. of two positive numbers a and b, (agtb) , is twice their G.M., then a:b is :

    A
    `2:sqrt3`
    B
    `2:7+4sqrt3`
    C
    `2+sqrt3:2-sqrt3`
    D
    `7+4sqrt3:7-4sqrt3`

  • The A.M., G.M. and H.M. between two positive numbers a and b are equal, then

    A
    a = b
    B
    ab = 1
    C
    `a gt b`
    D
    `a lt b`

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    If the ratio of A.M.between two positive real numbers a and b to their H.M.is m:n then a:b is equal to

    It the A.M., is thrice the G.M. of two positive numbers . Show that numbers are in the ratio (3 pm 3 sqrt(2))/(3 - 2 sqrt(2))

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    If sum of two numbers a&b is n xx their G.M then show that (a)/(b)=(n+sqrt(n^(2)-4))/(n-sqrt(n^(2)-4))

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