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 stuart clark March 5th, 2011 07:03 PM

Maximum value

If $x,y,z\in \mathbb{R}$ and $x+y+z= 0$ and $x^2+y^2+z^2= 6$. Then $Max.(x^2y+y^2z+z^2x)$

 neo March 5th, 2011 09:58 PM

Re: Maximum value

Look at the 'integer solutions' section of:

http://www.wolframalpha.com/input/?i=x^2+%2B+y^2+%2B+z^2+%3D+6+and+x%2By%2Bz%3D0

Calculate the value of the expression for each set of solutions

 MarkFL March 5th, 2011 10:02 PM

Re: Maximum value

So that folks will not have to copy and paste the URL into their browser:

 skipjack March 5th, 2011 10:56 PM

The variables are not required to be integers! The expression is to be maximized, not minimized.

The maximum seems to be 6, achieved when x, y and z are the zeros of r³ - 3r + 1.

 stuart clark March 11th, 2011 07:08 PM

Re: Maximum value

skipjack you are saying right.

explanation plz.

thanks

 johnny March 11th, 2011 07:10 PM

Quote:
 Originally Posted by stuart clark skipjack you are saying right.
Always. (Assuming not IMO problems)

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