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### A PROBLEM

Posted: Sun Dec 26, 2010 1:37 pm
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\[x_{1}^{3}+x_{2}^{3}+x_{3}^{3}+x_{4}^{^{3}}.\]

### Re: A PROBLEM

Posted: Sun Dec 26, 2010 2:15 pm
Are all of \$x_1,x_2,x_3,x_4\$ real ?

### Re: A PROBLEM

Posted: Sun Dec 26, 2010 5:35 pm
yap.They all are real.

### Re: A PROBLEM

Posted: Sun Dec 26, 2010 5:46 pm
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\$

### Re: A PROBLEM

Posted: Sun Dec 26, 2010 6:11 pm
oops.There was 1 in second line.

### Re: A PROBLEM

Posted: Sun Apr 08, 2018 8:44 am
prodip wrote:
Sun Dec 26, 2010 1:37 pm
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\[x_{1}^{3}+x_{2}^{3}+x_{3}^{3}+x_{4}^{^{3}}.\]
Get all three equations in the form
\[x_{1}+x_{2}+x_{3}=-(x_{4})\]
Similarly next,
Solve third equation by
\[a^3+b^3+c^3-3abc\]
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.