For which real numbers, a, does the equation
a 3^x + 3^{-x} = 3
have a unique solution?
multiply through by $\displaystyle 3^x$ and bring everything to one side, we get:
$\displaystyle a(3^x)^2 - 3 (3^x) + 1 = 0$
this is quadratic in $\displaystyle 3^x$. we can find its discriminant and from that we can tell what $\displaystyle a$ needs to be. (i assume you know what to look for. the discriminant must be equal to zero)
you may want to go further and solve for x