Math Help - Algebraic Exponents

1. Algebraic Exponents

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

2. Re: Algebraic Exponents

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

3. Re: Algebraic Exponents

Originally Posted by Espionage
If 3x + 3-x = 10/3 , the sum of the possible solutions is:
This problem is equivalent to $3y^2-10y+3=0$ where $y=e^x$.

4. Re: Algebraic Exponents

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: