Solve system of two equations with dependent variable

Posted 3 months ago
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 I want to solve the following system of two equations for $u$ and $v$ but can't figure out how to input it into WolframAlpha. $$\sum_{i=1}^{n} \frac{x_i-u}{v} = 0$$ $$-\frac{n}{2v}+\sum_{i=1}^{n} \frac{(x_i-u)^2}{2v^2} = 0$$The results I try to get from WA are $$u = \frac{1}{n} \sum_{i=1}^n x_i$$ $$v = \frac{1}{n} \sum_{i=1}^n (x_i - u)^2$$These are done by hand but want to know how to solve similar equations with WA.The problems are that I don't know how to write the $x_i$ (x_i in $\LaTeX$) and also don't know how to input the system of two equations. I know I can do this: https://www.wolframalpha.com/input/?i=system+of+two+equations and input them there, but then I can't specify what to solve them for.
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Posted 3 months ago
 Try solve (x1-u+x2-u+x3-u+x4-u)/v=0, -4/(2 v)+((x1-u)^2+(x2-u)^2+(x3-u)^2+(x4-u)^2)/(2 v^2)=0 for u,v hereWAIf you study the form of that solution carefully then I think that might let you realize the form of the solution for general n. You can extend that example to include x5 and see that the form of the solution persists.I believe there are two typos in your desktop published equations, in both cases you are summing over n from 1 to n when those should almost certainly be summing over i from 1 to n.If you absolutely must give your problem to WolframAlpha in Latex and you must pose your problem for abstract values of n then perhaps someone else can help you with that, those are far beyond me.