# Math Help - complex number question 1

1. ## 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 $z=4y^3-3y$

2. 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.