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Math Help - For which real numbers

  1. #1
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    For which real numbers

    For which real numbers, a, does the equation

    a 3^x + 3^{-x} = 3

    have a unique solution?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by perash View Post
    For which real numbers, a, does the equation

    a 3^x + 3^{-x} = 3

    have a unique solution?
    multiply through by 3^x and bring everything to one side, we get:

    a(3^x)^2 - 3 (3^x) + 1 = 0

    this is quadratic in 3^x. we can find its discriminant and from that we can tell what a needs to be. (i assume you know what to look for. the discriminant must be equal to zero)

    you may want to go further and solve for x
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