Algebraic Exponents

If 3^x + 3^-x = 10/3 , the sum of the possible solutions is:

Hint: f(x)=3^x+3^-x is an even function meaning that f(x)=f(-x)

Quote:

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Originally Posted by Espionage

If 3^x + 3^-x = 10/3 , the sum of the possible solutions is:

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This problem is equivalent to $\displaystyle 3y^2-10y+3=0$ where $\displaystyle y=e^x$.

Hi Espionage,
The easiest solution is to notice "by inspection" that 1 and -1 are roots. So the sum is 0. I'm not really that much of an arithmetic whiz. I drew the graph and then realized from the graph that 1 and -1 are the roots. Moral: always draw a picture if you can. Of course, use technology to draw said picture. Here's the graph that I drew together with the solutions as suggested above:

Attachment 28697