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[tex]2x+2y+2z-3=0[/tex]

[tex]x^3+3yz^2-u=0[/tex]

[tex]y^3+3x^2z-u=0[/tex]

[tex]z^3+3xy^2-u=0[/tex]

Problem questions:

a)Is the quadruple

**(1/2,1/2,1/2,1/2)**the only solution to the system in [tex]\mathbb{R}_{+}[/tex] ?

b)If the answer to a) is "yes" how to proove that fact;if the answer is "no" how to determine how many other (nonelementar) solutions the system of equations like that will have ?