# For which real numbers

• September 14th 2008, 03:16 PM
perash
For which real numbers
For which real numbers, a, does the equation

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

have a unique solution?
• September 14th 2008, 03:25 PM
Jhevon
Quote:

Originally Posted by perash
For which real numbers, a, does the equation

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

have a unique solution?

multiply through by $3^x$ and bring everything to one side, we get:

$a(3^x)^2 - 3 (3^x) + 1 = 0$

this is quadratic in $3^x$. we can find its discriminant and from that we can tell what $a$ 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