A PROBLEM

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prodip
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A PROBLEM

Unread post by prodip » 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\[x_{1}^{3}+x_{2}^{3}+x_{3}^{3}+x_{4}^{^{3}}.\]
Last edited by prodip on Sun Dec 26, 2010 6:09 pm, edited 1 time in total.

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Zzzz
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Re: A PROBLEM

Unread post by Zzzz » Sun Dec 26, 2010 2:15 pm

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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prodip
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Re: A PROBLEM

Unread post by prodip » Sun Dec 26, 2010 5:35 pm

yap.They all are real.

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Zzzz
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Re: A PROBLEM

Unread post by Zzzz » 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 $x_1=x_2=x_3=x_4=0$
Every logical solution to a problem has its own beauty.
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prodip
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Re: A PROBLEM

Unread post by prodip » Sun Dec 26, 2010 6:11 pm

oops.There was 1 in second line.

Mathlomaniac
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Re: A PROBLEM

Unread post by Mathlomaniac » 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.

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