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Thread: complex number question 1

  1. #1
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    complex number question 1

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