Equidistant Points from P & Q in 3D Space

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Let P=(–5,7,6) and Q=(–6,–4,2). The set of all points that are equidistant from P and Q has the equation=?
 
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What have you tried?

If you haven't tried anything, you might start with a point (x, y, z) that is one of the set of points equidistant from the two given points. Do you know a formula for distance in 3-D space?
 
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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