Solving 0 in Physics E&M Equation

[anonymity]

I am working on a physics problem from a calc-based E&M (intro) course, and I came up with the following equation:

E = 0 = 10 / (1 - x)² + 5 / x² - 10 / (1 + x)²

I got here and worried it was a dead end, so I checked the solutions manual, and they have the exact same thing, and then say " therefore, the root is bla. So, ~equation~ = 0 => x = bla"

How did they solve this? =|

edit: The only attempt I would know how to make is solve one of the terms individually, and then solve the other two as a system, and hope that one of the two solutions coincide. However, this seems stupid because that basically leaves it all to chance.

 

[micromass]

Hi anonymity!

Put the fractions on the same denominator and add them up. That's always a good first step!

 

[Mark44]

Not a major point, but your title is screwy. You never "solve for zero." We know what zero is. You're solving for x, which is not known.

 

[anonymity]

Yeah I know I read that as I was closing out the window to head to class..didn't have time or motivation enough to edit it, as it is irrelevant and clarified in my post.

Micro: thanks ill try that, seems like it could get very messy very quick though : I

 

[Ray Vickson]

I am working on a physics problem from a calc-based E&M (intro) course, and I came up with the following equation:

E = 0 = 10 / (1 - x)² + 5 / x² - 10 / (1 + x)²

I got here and worried it was a dead end, so I checked the solutions manual, and they have the exact same thing, and then say " therefore, the root is bla. So, ~equation~ = 0 => x = bla"

How did they solve this? =|

edit: The only attempt I would know how to make is solve one of the terms individually, and then solve the other two as a system, and hope that one of the two solutions coincide. However, this seems stupid because that basically leaves it all to chance.

Did they give a formula, or a numerical answer? If they gave a formula, what is it?

If they give a formula they might have used the general solution of a quartic equation as given in http://en.wikipedia.org/wiki/Quartic_function , for example. If they gave a numerical answer they might have used Newton's Method.

RGV

 

[anonymity]

It was a numerical value. I can't believe I didnt think of using Newton's method (i can't believe, either, that this actually showed up in a class other than basic single variable calculus...).

As far as if this is the way the book did it, I am not so sure. It seems unlikely that they would REQUIRE you to use something as obscure as Newton's method for a general physics course.

Regardless, assuming Newton's method doesn't fail and bounce all around the number plane, it will work. I will ask my professor tomorrow if there's a less tedious/more basic way to solve it.

Thanks for your help Ray.