If \[x_{1}+x_{2}+x_{3}+x_{4}=0 \] and
\[x_{1}^{2}+x_{2}^{2}+x_{3}^2+x_{4}^{2}=1 \] Then what is the biggest value of\[x_{1}^{3}+x_{2}^{3}+x_{3}^{3}+x_{4}^{^{3}}.\]
A PROBLEM
Re: A PROBLEM
Are all of $x_1,x_2,x_3,x_4$ real ?
Every logical solution to a problem has its own beauty.
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Re: A PROBLEM
I think there is a typo in your problem. You have written: \[x_1^2+x_2^2+x_{3^2}+x_4^2=0\]. Probably it should be \[x_1^2+x_2^2+x_3^2+x_4^2=0\]
Then, its clear that $x_1=x_2=x_3=x_4=0$
Then, its clear that $x_1=x_2=x_3=x_4=0$
Every logical solution to a problem has its own beauty.
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Re: A PROBLEM
oops.There was 1 in second line.

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Re: A PROBLEM
Get all three equations in the form
\[x_{1}+x_{2}+x_{3}=(x_{4})\]
Similarly next,
Solve third equation by
\[a^3+b^3+c^33abc\]
And in next take an equation of which \[x_{1},x_{2},x_{3}\] are roots of the equation to find product of the three.