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i couldn't do the following question for hours

minimize $\sum_{i=1}^{n}x_{i}^{3}$

s.t. $\sum_{i=1}^{n}x_{i}=0$ and $\sum_{i=1}^{n}x_{i}^{2}=n$.

by Lagrange multiplier rule

?

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    I am *sure* there is an example of using Lagrange multipliers with two constraints in pretty much *any* calculus textbook (Google gives me, for the obvious query, a list of results such that I find such examples in 4 of the first 5 results) Try to follow any such example out there, explain to us what you did and then we can help you with what you were not able to do.2010-10-20
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    i made my lagrange function as a0(x1^3+...+xn^3)+a1(x1+...+xn)+a2(x1^2+...xn^2) where a0, a1, a2 are lambda 0, 1, 2 then i take partial derivative for xi's (dL/dxi)=a0(3xi^2)+a1+2a2(xi)=02010-10-20
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    i made my lagrange function as a0(x1^3+...+xn^3)+a1(x1+...+xn)+a2(x1^2+...xn^2) where a0, a1, a2 are lambda 0, 1, 2 then i take partial derivative for xi's (dL/dxi)=a0(3xi^2)+a1+2a2(xi)=0 i now i have n such equations and 2 constraints but i cannot eliminate a1 and a2 to get a relation between xi's. so what can i do?2010-10-20
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    Your question $\min f(x_{1},x_{2},\ldots ,x_{n})=\sum_{i=1}^{n}x_{i}^{3}$ s.t. $% \sum_{i=1}^{n}x_{i}=0$ and $\sum_{i=1}^{n}x_{i}^{2}=n$ is equivalent to find $\min f(x_{1},x_{2},\ldots ,x_{n-1})=-\left( \sum_{i=1}^{n-1}x_{i}\right) ^{3}+\sum_{i=1}^{n-1}x_{i}^{3}$ s.t. $\left( \sum_{i=1}^{n-1}x_{i}\right) ^{2}-n+\sum_{i=1}^{n-1}x_{i}^{2}=0.$.2010-10-20
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    Why don't you explain that in the body of the question, writing down the system of equations you got in detail, and change the title to "how do I solve this system of equations?". From what you wrote, it is clear that you don't have any problems with Lagrange multipliers :)2010-10-20
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    Shouldn't the title be " ... for 2 ..." instead of " ... for more than 2 ..."?2010-10-23

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