Expression (x^3)y + (y^3)z + (z^3)x

 
 
Show that for all real numbers   x, \; y, \; z   such that

x \; + \; y \; + \; z \; = \; 0

and

x \, y \; + \; y \, z \; + \; z \, x \; = \; -3
 

the expression   x^3 \, y \; + \; y^3 \, z \; + \; z^3 \, x   is a constant.

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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