# Algebraic Exponents

• Jun 29th 2013, 01:39 PM
Espionage
Algebraic Exponents
If 3x + 3-x = 10/3 , the sum of the possible solutions is:
• Jun 29th 2013, 01:58 PM
Shakarri
Re: Algebraic Exponents
Hint: f(x)=3x+3-x is an even function meaning that f(x)=f(-x)
• Jun 29th 2013, 02:27 PM
Plato
Re: Algebraic Exponents
Quote:

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 $y=e^x$.
• Jun 29th 2013, 06:06 PM
johng
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:

Attachment 28697