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Math Help - complex number question 1

  1. #1
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    complex number question 1

    Given that 2y=a^x+a^{-x} , where a >1 and x>0 , prove that a^x=y+\sqrt{(y^2-1)} . Similarly , if 2z=a^3x+a^{-3x} , prove that z=4y^3-3y
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  2. #2
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    Note that 2y = a^x + a^{ - x} \, \equiv \,a^{2x} - 2ya^x + 1 =0.
    If you can solve z^2 -2yz +1 =0 for z, you can do the first part.
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