Solve $2^x+2^{-x} = 2$ Need to solve:

$$2^x+2^{-x} = 2$$

I can't use substitution in this case. Which is the best approach?

Event in this form I do not have any clue:

$$2^x+\frac{1}{2^x} = 2$$
Elucidate the problem by using the substitution $u = 2^x$, then you have $$u + \frac{1}{u} = 2$$

Multiply throughout by $u \neq 0$ to get $$u^2 +1 = 2u \iff u^2 - 2u + 1 = 0$$

This is an easy quadratic to solve, you should get $u = 1$ and hence you need only solve $2^x = 1 \iff x = 0$.
$$2^x =y $$
$$y+ \frac{1}{y} =2$$ 
Using AM-GM INEQUALITY
$$\frac{({y+ \frac{1}{y}})}{2} \ge \sqrt {y.\frac{1}{y}}$$

$$y+ \frac{1}{y}\ge 2$$