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Math Help - find the sum of all real roots

  1. #1
    Member grgrsanjay's Avatar
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    find the sum of all real roots

    find the sum of all real roots of this equation
    x + \frac{x}{\sqrt{x^2 - 1}} = 2010

    i think no real roots exist and may be the answer is 0

    i got options even
    (A)2010
    (B)4040
    (C)1005
    (D)0
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  2. #2
    Super Member Failure's Avatar
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    Quote Originally Posted by grgrsanjay View Post
    find the sum of all real roots of this equation
    x + \frac{x}{\sqrt{x^2 - 1}} = 2010

    i think no real roots exist and may be the answer is 0
    No, I think it is likely that there are two real roots.
    For consider: for x large you have that the second term on the left side is about 1, so you would expect one real solution to be close to 2009.
    Also, for x tending to 1 from the right you have that the value of the left side goes to +oo. Hence you can expect another real root to be found close to 1 (but greater than 1).

    i got options even
    (A)2010
    (B)4040
    (C)1005
    (D)0
    Based on my above guesswork I would say that option (A) is right.
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