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?

You haven't done anything wrong! To complete your answer, one way you can see the answer is $6$ is to guess that
$$17 + 12 \sqrt{2} = (a + b\sqrt{2})^2$$
Giving us
$$17 = a^2 + 2b^2, \ \ ab = 6$$
Giving us 
$$a = 3, \ \ b = 2$$
Thus $$ \sqrt{17 + 12 \sqrt{2}} = 3 + 2\sqrt{2}$$ 
which gives $$2^x + 2^{-x} = 6$$
(And similarly for $17 - 12\sqrt{2}$)
A simpler way is to notice that $(2^x + 2^{-x})^2 = 4^x + 4^{-x} + 2$.
