$x = 1+2^p$ $y= 1+2^{-p}$ Finding the $y$ in terms of $x$. $$x = 1+2^p$$ $$y= 1+2^{-p}$$ Find the $y$ in terms of $x$.


What if I combine these 2 equations?

$$x+y = 1 + 2^p + 2^{-p}$$

It seems like that there will be no solution from there.
Put $2^p$ from one equation to other  

$y=1+2^{-p} = 1 + \cfrac{1}{x - 1}$
write $$x-1=2^p$$ and $$y-1=2^{-p}$$ by multiplication we obtain $$(x-1)(y-1)=1$$ since $$2^p\cdot 2^{-p}=1$$