From Conservative Vector Field to Potential Energy function

bingo92
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What if when I'm finding the repeated terms from integrating the vector field with respect to x and then y, i come across two terms that are same except one is negative and the other positive. What does that mean, and how do i represent that in the overall potential function I'm finding?
 
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I have no clue what you mean by "two terms that are same except one is negative and the other positive". Could you post a specific example?
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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