If $4^x + 4^{-x} = 34$, then $2^x + 2^{-x}$ is equal to...? I am having trouble with this:

If $4^x + 4^{-x} = 34$, then what is $2^x + 2^{-x}$ equal to? 

I managed to find $4^x$ and it is:
$$4^x = 17 \pm 12\sqrt{2}$$
so that means that $2^x$ is:
$$2^x = \pm \sqrt{17 \pm 12\sqrt{2}}.$$
Correct answer is 6 and I am not getting it :(. What am I doing wrong?

Let $a=2^x$. Then $2^{-x}=1/a$ and $$\left(a+\frac1a\right)^2=a^2+2+1/a^2=2+(2^x)^2+(2^{-x})^2=2+4^x+4^{-x}=2+34=36.$$ This means that $a+1/a=6$ (it should be 6 or -6, since these are the square roots of $36$ but since $a$ and $1/a$ are positive, it is 6).
