For which real numbers, a, does the equation

a 3^x + 3^{-x} = 3

have a unique solution?

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- Sep 14th 2008, 03:16 PMperashFor which real numbers
For which real numbers, a, does the equation

a 3^x + 3^{-x} = 3

have a unique solution? - Sep 14th 2008, 03:25 PMJhevon
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