For which real numbers, a, does the equation
a 3^x + 3^{-x} = 3
have a unique solution?
multiply through by and bring everything to one side, we get:
this is quadratic in . we can find its discriminant and from that we can tell what 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