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 March 5th, 2011, 07:03 PM #1 Member   Joined: Jan 2011 Posts: 40 Thanks: 0 Maximum value If $x,y,z\in \mathbb{R}$ and $x+y+z= 0$ and $x^2+y^2+z^2= 6$. Then $Max.(x^2y+y^2z+z^2x)$
 March 5th, 2011, 09:58 PM #2 Member   Joined: Feb 2011 Posts: 79 Thanks: 0 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 The maximum value is your answer
 March 5th, 2011, 10:02 PM #3 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Maximum value So that folks will not have to copy and paste the URL into their browser: click here
 March 5th, 2011, 10:56 PM #4 Global Moderator   Joined: Dec 2006 Posts: 20,978 Thanks: 2229 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.
 March 11th, 2011, 07:08 PM #5 Member   Joined: Jan 2011 Posts: 40 Thanks: 0 Re: Maximum value skipjack you are saying right. explanation plz. thanks
March 11th, 2011, 07:10 PM   #6
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Quote:
 Originally Posted by stuart clark skipjack you are saying right.
Always. (Assuming not IMO problems)

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